Systems and methods for enhancing and developing new games and activities based on logical puzzles.

Abstract

A computer system provides a method and apparatus for associating a label with an execution order of steps in solving a puzzle, game, or activity for one or more portions of one or more solution paths of the puzzle, game, or activity. In associating a label with an execution order of steps to solve a puzzle, game, or activity, the execution of the puzzle solution as well as the specific order of steps in the solution path are used to evaluate the efficiency of one sequence of steps relative to another. Quantifying the efficiency of the solution path allows for a logical and objective comparison of the efficiency of two or more solutions or completions of a puzzle, game, or activity.

Description

[Technical Field]

[0001] Cross-reference of related applications This application is a continuation of U.S. Patent Application No. 13 / 843,844 "ENHANCING TECHNIQUES AND SYSTEMS FOR LOGICAL GAMES, ACTIVITIES AND PUZZLES" filed on March 15, 2013, and U.S. Patent Application No. 15 / 233,798 "ENHANCING TECHNIQUES AND SYSTEMS FOR LOGICAL GAMES, ACTIVITIES AND PUZZLES" filed on August 10, 2016, claiming priority to U.S. Patent Provisional Application No. 61 / 794,208 "ENHANCING TECHNIQUES AND SYSTEMS FOR LOGICAL GAMES, ACTIVITIES AND PUZZLES" filed on March 15, 2013, and U.S. Patent Provisional Application No. 61 / 799,975 "NOVEL APPLICATIONS OF LOGICAL GAMES, ACTIVITIES AND PUZZLES" filed on March 15, 2013, under Section 119(e) of the U.S. Patent Act, and U.S. Patent Application No. 13 / 843,844 "ENHANCING TECHNIQUES AND SYSTEMS FOR LOGICAL GAMES, ACTIVITIES AND PUZZLES" filed on March 15, 2013, and U.S. Patent Provisional Application No. 61 / 799,975 "NOVEL APPLICATIONS OF LOGICAL GAMES, ACTIVITIES AND PUZZLES" filed on March 15, 2013, and U.S. Patent Application No. 13 / 843,844 "ENHANCING TECHNIQUES AND SYSTEMS FOR LOGICAL GAMES, ACTIVITIES AND PUZZLES" filed on March 15, 2013 This document claims the interests of U.S. Patent Application No. 17 / 168,139, "SYSTEMS AND METHODS TO ENHANCE AND DEVELOP NEW GAMES AND ACTIVITIES BASED ON LOGIC PUZZLES," filed on February 4, 2021, which is a continuation of U.S. Patent Application No. 15 / 985,723 (currently U.S. Patent No. 10,933,323), "SYSTEMS AND METHODS TO ENHANCE AND DEVELOP NEW GAMES AND ACTIVITIES BASED ON LOGIC PUZZLES," filed on 22 May 2018, which is a continuation of "TECHNIQUES AND SYSTEMS FOR LOGICAL GAMES, ACTIVITIES AND PUZZLES," and all the contents of each of those applications are incorporated herein by reference.

[0002] This disclosure relates to games and activities with skills and logic that can be modeled by logic puzzles, in addition to a particular area of logic puzzles, which is a special focus of this application.

Background Art

[0003] Logic games, skill and strategy games, puzzles, and similar activities have been used in many cultures for thousands of years for social and educational purposes as well as entertainment. In addition to puzzles of particular interest, many games and activities belong to the class where the methods and systems disclosed by the present invention are envisioned, and the reference to "activity" herein includes games and puzzles unless otherwise excluded. Certain variations of physical activities and team sports are also considered to belong to the targeted class.

[0004] Games and activities in the targeted class may be cooperative or competitive and are characterized by subordinate activities, i.e., "steps". A participant or player can proceed to the "next step" or one of several possible "next steps" by making decisions based on knowledge about the activity, the state of the activity up to the moment of taking a step, general knowledge about other players and the environment, the player's skills, the logical "validity" of the next one or more steps, and such other factors. The factors of skill and logical validity distinguish the problems of this class from games and activities of pure chance, although elements of chance may also be included as additional determining factors for the targeted class of activities.

[0005] Games and puzzles involving skill and logic are the subclasses covered. Various types of crosswords, word scrambles, and number puzzles are categories of particular interest. Many such activities are popular and are published daily in various media, including print and the internet. The number / logic puzzle "Sudoku" is the best-known example of the class of logic puzzles to which the methods of this invention apply. However, these methods are applicable to a much broader class of logic puzzles and other activities with suitable adaptations.

[0006] Since the British newspaper The Times published the number / logic puzzle called "Sudoku" in 2004, it has enjoyed immense popularity. Alongside classics like crosswords and word scramble, it is now featured in newspapers and magazines worldwide, and numerous books have been published on the subject. Variations of Sudoku and other puzzles inspired by it have similarly gained popularity. Sudoku's popularity has even led to the development of television programs based on the idea of ​​contestants solving the puzzle live, encouraging viewers at home to participate. While Sudoku championships to determine the best Sudoku players have been held worldwide for several years, their popularity and viewership remain relatively limited. The methods and systems disclosed herein could potentially enhance the commercial and educational value of these events by providing new ways for television and internet audiences to participate.

[0007] Sudoku is the best-known example of the class of logic puzzles to which the method of this invention applies. However, this method is applicable to a much broader class of logic puzzles.

[0008] Generally, in this class of puzzle or problem, one or more players are given a structure containing many cells or spaces, and a collection of letters, often alphanumeric, and are asked to fill in the cells. Typically, one letter is placed in a space or cell according to a set of rules. Some cells may already have letters filled in by the puzzle creator at the start of the puzzle. If the letters are numbers, the rules may, but not necessarily, be based on mathematical principles. Similarly, in other cases, filling cells with letters may be semantically important, but not necessarily required by the rules. Hereafter, the words "cell," "square," and "space" are used synonymously unless otherwise specified.

[0009] The most common form of Sudoku puzzle consists of a grid of 81 cells arranged in a 9x9 grid, with 9 blocks stacked on top of each other. Each block is comprised of 9 adjacent cells (squares) arranged in a 3x3 grid, with some cells filled with numbers, but most being blank. The goal in this typical case is to fill the blank or empty squares / spaces or cells with the numbers 1 through 9 so that no numbers are repeated in any row, column, or within any 3x3 block containing any cells.

[0010] The popularity of Sudoku has led to the creation of a wide variety of new puzzles, including those using different sets of letters (for example, letters instead of numbers), different sized grids, altered layouts of spaces, or irregular grids. A puzzle called KenKen shares some rules with Sudoku, but while Sudoku does not require any knowledge of mathematical operations, KenKen's rules rely on arithmetic calculations to fill in the blank cells.

[0011] The above and other variations are suitable for the methods of some embodiments of the present invention and are included in the class of puzzles assumed therein. These methods can be adapted to the above and such other variations by using the details described herein with respect to Sudoku.

[0012] The discussion and description herein focus particularly on logical puzzles, games, and activities that end in a unique solution or goal, and propose novel methods for distinguishing solutions by different players in such activities. [Overview of the project] [Problems that the invention aims to solve]

[0013] This invention addresses two problems related to the activities described above that frequently occur in the real world, by presenting exemplary embodiments. (1) When the outcome or final solution is unique, how can you distinguish between two or more completed activities, games, or attempts to complete an activity, game, or puzzle? (2) How can participants in a competitive or collaborative activity, game, or puzzle be selected, ranked, or rewarded when the outcome or final solution is not distinguishable?

[0014] Currently, in competitions for solving logic puzzles such as Sudoku, the second problem is addressed by rewarding the participant who solves the puzzle in the shortest time. However, this is a method with many limitations and does not necessarily reward the most logical and insightful solution to the logic puzzle.

[0015] In conventional techniques, when a logic puzzle has a unique correct solution, such as Sudoku or KenKen, methods for prioritizing one solution over another (for example, in a contest) typically involve timing the solutions of two or more participants and selecting the fastest path as the "winner." However, this race-like method of selecting a contest winner ignores other possible differences between the paths to the solution taken by the participants.

[0016] The order in which steps are performed when solving puzzles such as Sudoku or KenKen can serve as a very useful parameter for distinguishing between multiple solution paths, and the methods disclosed herein demonstrate that they can be used as an alternative to or in addition to conventional time-based criteria for selecting a “winning” solution path.

[0017] The answer presented by some embodiments of the present invention is to logically distinguish the solutions of puzzles, games, and activities of interest based on the order in which the steps leading to the completion of the activity are performed. For simplicity of explanation, this specification uses specific examples of puzzles with unique solutions. A similar approach can be applied to activities that can be modeled by such puzzles.

[0018] Methods according to some embodiments of the present invention work by considering not only the execution of each step of an activity or problem, but also the exact sequence of steps in solving or completing the activity. An activity may reach two similar goals through two different sets of steps, but one set of steps may be considered "preferred" to the other, partly based on the relative efficiency of the other set of steps. Thus, this disclosure relies on the view that the efficiency of two or more solutions or completions of a puzzle, game, or activity can be logically and objectively compared if the "efficiency" of the exact solution or execution sequence of the puzzle, game, or activity can be quantified.

[0019] This patent application and its prior applications describe a method for "quantifying" differences in the logical order of steps in solving a puzzle, along with a device for tracking the order of steps by associating them with labels whose order is known. Thus, measurable logical differences between two or more sets of solution steps can be captured in a practical, meaningful, and time-independent manner by codifying the following assumption: a "shorter overall sequence" of steps to solve a puzzle is more efficient than a solution requiring a longer sequence of steps. The expression "shorter overall sequence" will be clarified in the following explanation.

[0020] In this application and related applications, the execution order of solution steps is tracked and used by associating labels with solution steps. Previous applications have indirectly provided hints based on the execution order of solution steps for two or more solution paths (e.g., the order of “contest winner”), but this application discloses a specific manner of generating hints, including hints based on the synthesis of associations of labels for all available valid solution paths.

[0021] The methods of the present invention have many real-world applications. For example, various embodiments thereof can, among other things, provide hints to novice players for solving puzzles without revealing the entire solution; enable the creation of hinted puzzles with particular educational utility; provide artists with new creative ways to capture and represent the structure of puzzles; generate other puzzles and activities from known puzzles; and provide opportunities for rewarding, skill-based online gambling games and activities for entertainment, as well as opportunities to foster interest in numbers and mathematical relationships.

[0022] In some embodiments (for example, a specific answer to a problem that generates hints for a new player to solve a puzzle), this technique relies on data from other completed solutions of the puzzle (usually by other players) by tracking the order in which each solution step was performed. This technique improves the method of (giving hints) by combining past solutions, ensuring that no valid solutions provided are discarded.

[0023] This method has several advantages for puzzles of actual interest, including: (i) all contest participants' labeling and insights are incorporated into the hints; (ii) hints can stabilize more quickly; (iii) the synthesis of "objective" labeling of steps incorporates a kind of "smoothing" into labels from various paths; (iv) for people solving the puzzle for the first time, hints based on the synthesis of "objective" labeling for solution steps are more useful than hints based on labels from the "smartest" path; and (v) the invention is more clearly applicable to the actual scenarios it is envisioned for (i.e., when various solutions are provided via networked computer equipment, labels indicating the order in which steps are performed (e.g., filling in empty spaces) need to be generated by the computer system).

[0024] In some of the embodiments of the anticipated real-world scenarios, by providing the puzzle on a website over a period of time (several days or weeks), complete solutions can be collected along with records of the order in which the blank spaces are filled and other relevant data. Furthermore, it is expected that multiple participants will provide numerous solutions for each puzzle. After the period ends, the system of the present invention processes all the solutions provided by the many participants, removing any solutions that contain one or more errors, such as incorrect order in which the blank spaces are filled. Thus, a subset of logically error-free solutions is retained.

[0025] Then, after "synthesizing" the space filling order from all logically correct answers, the system generates hints using the synthesized space filling order.

[0026] In the case of puzzles of interest, it is expected that the number of empty spaces to be filled often far exceeds the number of hints. Due to the need to assist new players (humans) in solving the puzzle and avoid overloading human senses (such as vision and hearing) through specific display of hints, differences such as colors or sounds adopted as hints should be limited. On the other hand, the number of spaces to be filled in puzzles of interest is usually not limited. Also, it is important to provide hints that human players can actually use.

[0027] Therefore, this arithmetic system needs to be programmed to make appropriate decisions in order to cope with the human psychological boundary with the puzzle complexity.

[0028] This disclosure introduces a new logical composition and structure including a quantitative measure that can be used for a logic-based comparison independent of the time to complete two or more activities based on the puzzle structure (e.g., the number and type of characters or pieces, and their distribution in each puzzle matrix). Thus, for example, a logically inferred solution is considered more efficient (i.e., preferable) than a "brute force" trial-and-error approach of trying every number in all empty cells of a Sudoku puzzle to find the one correct number for that cell.

[0029] Many scenarios to which the method of the present invention can be applied involve comparing different attempts for completing an activity or solving a puzzle, but may also involve comparing parts or segments of these attempts, or other similar descriptors. To facilitate such comparisons, the quantitative configuration disclosed in prior related applications is an algorithmically calculated “measure of efficiency” of a solution or execution that takes into account the execution of the process from start to finish of a given game, puzzle, or activity, in conjunction with information on the actual sequence of steps performed between the start and the goal for a given solution or execution.

[0030] A “measure of efficiency” is a quantitative descriptor of a set of steps in an activity, game, or puzzle of interest, used to calculate the progress of that set of steps. Therefore, the calculation involves some variation of the following operations: (1) providing an algorithm or mechanism for tracking the order in which the steps of an activity are performed toward the goal of completing the activity; (2) associating an indicator with each step of the activity to annotate points in the order in which the steps are performed; (3) associating a quantity (e.g., a real number) with each step of the activity by the use of the indicator; and (4) obtaining a numerical measure by a suitable formula, through a combination of the quantities associated with each step in that order.

[0031] Comparing two or more sets of steps involves two additional steps: (5) assigning a measure of efficiency to each of the two or more sets of steps, and (6) comparing different sets of steps using the numerical measures of efficiency calculated for each.

[0032] Furthermore, the order derived from the comparison of these calculated numerical scales allows for arbitrary priority selection from two or more orders.

[0033] The present invention represents a novel trial that addresses two problems: (1) how can two or more completions or attempts to complete an activity, game, or puzzle be distinguished when the ending or final solution is unique? and (2) how can rewards be set for competitive or cooperative activities, games, or puzzles when the ending or final solution is unique?

[0034] To address these issues, this disclosure introduces a new logical structure and framework that includes quantitative measures that can be used to logically compare the completion of two or more activities. Such activities can be performed or demonstrated on television, and are equally common on the internet, due to their respective popularity. Furthermore, as will be discussed later in this specification, these activities can generally bring many other benefits in a wide range of fields, from education to cryptography.

[0035] For example, despite Sudoku's immense popularity and the backing of supporters such as the BBC and the New York Times, attempts to televise Sudoku competitions remain relatively uncommon. This may be partly due to the lack of interesting models for active audience participation or participation via the internet.

[0036] The structures and standards provided by this invention can be used, among other things, to create novel games, puzzles, and activities via special digital devices and / or the Internet for a wide variety of activities, as well as to generate interesting models for audience participation. This endeavor has the potential to create entirely new industrial fields.

[0037] Currently, Sudoku solving competitions are often held in real time with live audiences. While the audience can watch each competitor's process of arriving at the solution, the players themselves cannot see each other's work in progress. Winners are chosen based on the time it takes to arrive at a uniquely correct solution, much like in athletic competitions. Treating an activity as a time-based competition in this way is unsatisfying for many reasons.

[0038] This method neither rewards competitors for having superior logical reasoning in solving a "logical" puzzle compared to another competitor, nor does it showcase the logical reasoning employed by the competitors to the audience. The audience misses the opportunity to appreciate the symphony of "logical artistry" that can be employed when solving Sudoku or similar logical puzzles.

[0039] Since time is a measurable quantity, it is easy to adopt as a determinant for selecting a winner. Currently, this is the only determinant, given the lack of a quantitative / numerical measure that can capture whether one solution is logically superior to another. This invention thus presents a measurable quantity. The methods and systems disclosed herein are based on a time-independent quantitative measure of logical "superiority," and such a measure can be used to select winners in competitions involving logical activities or puzzles such as Sudoku. However, if the competition organizer desires, time may also be used as an additional parameter for selecting a winner.

[0040] This approach starts from the view that a reliable measure of puzzle difficulty should be based on the puzzle's structure, namely the number and types of letters or pieces, and their distribution within each puzzle matrix.

[0041] Another possible view is that a valid way to determine the logical superiority of one solution to a puzzle over another is based on a calculation of how easily the spaces can be filled from the "start" of the solution. This means that a more direct solution, based on sufficient reasoning, is preferable and deserves to win, rather than a "serpentine" solution that takes more steps to achieve the same goal. Therefore, for example, when filling in the empty cells of a Sudoku puzzle, a logically reasoned solution is preferable to a "brute-force" trial-and-error method that tries every number in every empty cell until it fails to find the one number that fits in that cell.

[0042] Prior methods for selecting winners in games do not provide a quantitative measure that allows for the comparison of participants' proficiency in logical activities, including logical games and puzzles such as Sudoku, other than comparing the "race to the finish line." However, a race based on "time to the finish line" is an inappropriate and insufficient determinant for a class of activities that may aim to select winners based partly on logical reasoning ability.

[0043] In this sense, the "efficiency" of a solution correlates with the "complexity" of the puzzle. Solutions to simple puzzles generally become apparent in fewer overall steps, while solutions to complex puzzles require many steps to take shape, a fact that applies to players of all skill levels. Therefore, in a sense, the time it takes for a human or computer to solve a puzzle correlates with the complexity or difficulty of the puzzle. However, "time to solution" alone cannot capture the complexity or difficulty of a logical puzzle. This is because fluctuations due to external factors unrelated to the logical reasoning cannot be fully controlled by either a human or a computer when attempting to solve a puzzle.

[0044] On the other hand, the present invention enables meaningful comparisons of time-independent performance by introducing novel algorithmic processes and configurations for generating quantitative measures for solving puzzles or achieving activities in a target class.

[0045] Furthermore, the method of the present invention may enable the analysis of a puzzle or activity in terms of the "efficiency" of solving a logical problem. The method of the present invention provides at least one quantitative estimate of the complexity of the puzzle based on the efficiency of the solution. Such an estimate may be further improved by selecting the best estimate from solutions submitted by multiple "players" and arriving at an average value that is considered to be close to the best estimate.

[0046] In the case of puzzles such as Sudoku, algorithms for calculating a measure of efficiency, as disclosed herein, take into account the total number of cells or spaces in the puzzle, the number of "empty" cells to be filled, and the structure of the puzzle (including the set of characters used to fill the spaces and the distribution of characters that are initially filled in blank or non-empty spaces). Furthermore, such algorithms for calculating a measure of efficiency can be adapted to activities that can be modeled by logical puzzles.

[0047] The disclosure method for calculating the efficiency of a solution is even more useful because, conversely, it can be used to reveal the structure of a puzzle or activity. The present invention provides methods and systems for solving or completing a class of logic, skill, or reason-based activities, such as puzzles, games, or activities. It also provides a method for comparing two or more activity completion examples and ranking them in order of preference, which can also be used in collaborative or competitive searching for solutions to problems or completing activities, as well as creating other puzzles or activities.

[0048] Many other applications are conceivable by utilizing the central method presented herein. For example, this method can be used to determine the efficiency and relative proficiency of two or more players solving a puzzle, to provide various forms of a priori or dynamic hints to assist players attempting to complete a puzzle or activity, and to conduct internet-based cooperation or competition for solving puzzles or performing similar logic-based activities. Other conceivable applications include providing creative representations of puzzle solutions, displaying one or more solutions for the education or entertainment of viewers or audiences (including viewers or audiences on computer networks, or audiences at television or live shows), and publishing games, activities, and puzzles in various forms of media suitable for mass distribution, such as films, videos, CDs, DVDs, and other existing or future similar media.

[0049] Furthermore, this disclosure envisions and provides methods for novel creative representations of the solution or completion of an activity. Additionally, some forms of creative representation of an activity or problem may serve as inspiration for the construction of other puzzles, games, or activities for collaborative or competitive participation.

[0050] It is possible to calculate a measure of efficiency with respect to the solution or execution toward the goal or outcome of an activity. However, it is also meaningful to calculate a measure of efficiency toward a segment of the solution or execution, i.e., a series of steps from one point to another in the activity. Therefore, it is meaningful to calculate the efficiency of, for example, rows, columns, or blocks in a Sudoku puzzle.

[0051] Furthermore, it is possible to imagine the "optimal" efficiency of a solution, which can be defined as an attribute of the puzzle that cannot be surpassed by any path (series of steps) leading to the solution of the puzzle / activity. However, whether or not the optimal efficiency can be determined, it is reasonable to discuss the efficiency of one actual solution (path to it) by comparing it with another actual solution (path to it). One solution is considered highly efficient compared to another if its efficiency metric is superior.

[0052] Similar reasoning to that applied to Sudoku can be applied to other games and activities (including some games of chance) if it is possible to enumerate all possible steps following a preceding step. Therefore, if there can be an infinite number of steps or infinitely many possible sequences from a step, these games or activities are excluded.

[0053] In particular, in the case of logical puzzles, the possibilities of subsequent steps are usually finite, and therefore the order of steps leading to a conclusion is also limited. Accordingly, the methods disclosed herein can be usefully utilized in many ways, among others, such as solving puzzles to identify different solutions and thereby systematically generating new puzzles.

[0054] We explore quantitative measures for performing the activity steps in a specific order, and other suitable novel configurations and algorithms that achieve some of these goals are described in the detailed explanation below. [Brief explanation of the drawing]

[0055] [Figure 1] Figure 1 shows an example of a Sudoku puzzle. [Figure 2] Figure 2 shows an example of a solution to the Sudoku puzzle shown in Figure 1, using a method according to several embodiments. [Figure 3] Figure 3 shows another example of a Sudoku puzzle. [Figure 4] Figure 4 shows an example of a solution to the Sudoku puzzle shown in Figure 3, using a method according to several embodiments. [Figure 5] Figure 5 is a flowchart illustrating a method for ranking a series of steps in the execution of an activity, according to several embodiments. [Figure 6] Figure 6 is a diagram showing an exemplary computer system in which several embodiments of the present invention may be employed. [Figure 7] Figure 7 shows one modified example of a method applied to a crossword puzzle in Action Unlimited, a publication of a local advertiser in Massachusetts, according to several embodiments of the present invention. [Figure 8] Figure 8 shows one modified example of a method applied to an example of a number puzzle known as "Numbrix" according to some embodiments of the present invention. [Figure 9] Figure 9 visually shows the partial structure of the solution in Figure 2, where letters A, B, and C correspond to different graphic patterns. In this figure, the shaded filled cells are indicated by label C. The other cells are similarly filled with color, pattern, or animated graphics, etc. [Figure 10] Figure 10 shows an example of the KenKen puzzle. [Figure 11] Figure 11 shows a first example of a solution to the KenKen puzzle shown in Figure 10, using a method according to several embodiments, with alphabetical letter hints. [Figure 12] Figure 12 shows a second example of a solution to the KenKen puzzle shown in Figure 10, using a method according to several embodiments, with different alphabetical letter hints. [Figure 13] Figure 13 shows a third example of a solution to the KenKen puzzle of Figure 10, using a method according to several embodiments, further accompanied by another different set of alphabetical letter hints. [Figure 14] Figure 14 is a Sudoku puzzle. [Figure 15] Figure 15 shows the solution to the puzzle in Figure 14. [Figure 16] Figure 16 is a bar graph representing the solution to Figure 15. [Figure 17] Figure 17 is a compressed bar graph of the solution to Figure 15 using the 8-bar standard. [Figure 18] Figure 18 is another Sudoku puzzle. [Figure 19] Figure 19 shows the solution to the puzzle in Figure 18. [Figure 20] Figure 20 is a bar graph of the solution to Figure 19. [Figure 21] Figure 21 is a compressed bar graph of the solution to Figure 19 using the 8-bar standard. [Figure 22] Figure 22 is a diagram illustrating the logic for associating the partial filling of cells in the solution of Figure 11 with their labels. [Figure 23] Figure 23 is a diagram illustrating the logic for associating the partial filling of cells in the solution of Figure 12 with their labels. [Figure 24] Figure 24 is a diagram of a baseline flow for one embodiment of hint generation from the execution order of steps in multiple solution paths. [Figure 25] Figure 25 is a flowchart of the verification process using a system that associates puzzle-solving steps with labels. [Figure 26] Figure 26 illustrates the process of combining the labels of the puzzle-solving steps into a unified label. [Figure 27] Figure 27 is a flowchart of the process for associating solution steps with labels according to several embodiments. [Figure 28] Figure 28 illustrates computerized verification of solution paths and label assignments according to several embodiments. [Figure 29] Figure 29 shows an example of a Sudoku puzzle layout. [Figure 30] Figure 30 shows a partial solution to the puzzle in Figure 4 according to several embodiments, illustrating the label associations up to A and an example of determining letters and labels to fill a space (to fill a specific space) through trial and error. [Figure 31]Figure 31 is an example of a completed solution to the puzzle in Figure 4, showing the labels, the letters, and the logical reasoning for the label selection. [Figure 32] Figure 32 shows an exemplary blank layout of the puzzle, with a designated area for listing the steps of filling in the blank cells with possible characters (ordinal numbers indicating the order in which to fill the cells, labels associated with the fillings, the logical reasoning behind the label associations, and calculations if it is necessary to fill the cells using a trial-and-error method). [Modes for carrying out the invention]

[0056] The inventors have recognized that even when a puzzle has a unique final solution, it is possible to measurably distinguish between two or more paths to the solution by tracking the order in which the steps to solving the puzzle are performed.

[0057] Puzzles of this class, exemplified by Sudoku, fall under the more general category of constraint satisfaction problems (CSPs). Furthermore, it should be noted that activities that can be modeled by puzzles of interest may also exhibit differences in execution based on the order in which the steps are performed.

[0058] In a class of logical puzzles or problems to which the methods of multiple embodiments of the present invention apply, one or more players are given a structure containing many cells or spaces and a set of letters, often alphanumeric, and are asked to fill in the cells. Typically, one letter is filled into a space or cell according to a set of constraints and rules.

[0059] Therefore, we begin by demonstrating that (i) a mechanism can be formed to track the execution order of solution steps for puzzles, games, and activities in the target class, and (ii) that it is actually possible to obtain measurable quantities through such tracking.

[0060] This demonstrates that the execution order of puzzle-solving steps can be effectively tracked by associating steps with multiple of a set of labels whose order is known. Once the set of labels is available, a numerical value can be assigned to each label in the set, so that the order of the numerical values ​​corresponds to the order of the labels in the set, thus maintaining a strict one-to-one correspondence between the set of labels and the numerical values.

[0061] When such labels are associated with steps in the path to solving a puzzle, numerical values ​​are assigned to the execution steps via the labels. Then, by using the values ​​assigned to the steps in the path to the solution, quantitative aggregate measures can be calculated to represent the solution path. Furthermore, if the labels are defined to capture logical differences between solution paths, the logical differences between two different paths to the solution of a logical puzzle can be measurably distinguished by comparing the aggregate measures representing the two different paths. Moreover, the practical adoption of this method of distinguishing paths to the solution via labels allows for measurable distinction of logical differences even when the paths are unrelated or represent different puzzles.

[0062] The sequence of steps in solving a puzzle can be effectively tracked by associating multiple labels from a given set. The use of these labels provides a quantitative measure of logical differences between paths to solving a logical puzzle or between different types of puzzles. Furthermore, their use allows for providing hints for solving puzzles for educational and entertainment purposes, and offers a quantitative method for measuring and comparing "segments" of puzzle solutions.

[0063] For example, Sudoku games can be used as skill-based betting activities on the internet. Labels allow for measurements such as which row, column, or 3x3 box is filled first and second, which numbers are filled first in all rows, columns, or boxes, or which cells are filled in what order.

[0064] This activity can pique interest in logic through its use as a practical step.

[0065] Similarly, KenKen puzzles can be used to create interesting educational / mathematical activities for children.

[0066] How to associate solution execution steps with labels Starting with labels, all that is needed to track the execution order of each step in a solution using this method is a set of labels that have a predetermined or "natural" order to meaningfully describe the progression or "order" such as the execution order of the steps.

[0067] The Roman letters A, B, C, ... or the set of integers 1, 2, 3, ... are readily available sets that make sense in terms like "order," "preceding," or "succeeding," and should therefore be usable as labels. Thus, letters can be used as labels for steps in activities such as number-based Sudoku, and sets of integers can be used as labels in "word" Sudoku where the puzzle cells are filled with alphabetical letters.

[0068] Next, an algorithm for labeling the execution steps and inducing the order by Roman letters can be set up as follows:

[0069] Given a set of labels, associate the first label with the filling of any cell in the puzzle that can be filled based only on the given rules / constraints, and any given non-empty (pre-filled) cells. Next, associate the second label with the cells filled based on the given rules, pre-filled cells, and cells filled in association with the first label, and so on.

[0070] Therefore, for example, in the case of Sudoku, if the number in a cell is directly determined based only on the basic rules or constraints and the numbers given at the start of the puzzle, then the letter A is associated with the cell. If the filling is based on the basic rules, the information given at the start of the puzzle, and possibly one or more cells associated with A, but not on any cell associated with A or any letter following A in Roman letters, then the letter B is associated with the cell. If the filling is based on the given information and possibly one or more cells associated with B, but not on any cell associated with the letter C "greater than or equal to", then the letter label C is associated with the cell, and so on. To avoid circular reasoning, this algorithm can be described as a labeling rule as follows:

[0071] Rule: If cell filling is partially based on one or more cells associated with a character preceding the alphabetical character, but not on any cells associated with a character not preceding the (selected) character, then the alphabetical character is associated with the filling as a label.

[0072] This labeling rule is an addition to the usual basic rules for n x n Sudoku and can be described as follows:

[0073] Rule 1: Cells cannot be filled with numbers that are repeated within a row.

[0074] Rule 2: Cells cannot be filled with repeating numbers within a column.

[0075] Rule 3: For a given cell in an n x n grid, if all but one digit can be removed from the set 1 through n by Rule 1 or 2, then that cell can be filled with the one digit that is not removed.

[0076] Rules 1, 2, and 3 apply to many logic puzzles (including Sudoku and KenKen).

[0077] Rule 3 describes the following important practical point regarding puzzles of interest: Filling spaces or cells is a definitive action, but determining which numbers cannot be used to fill cells is a truly investigative act.

[0078] The association of labels with the steps to be solved through trial and error. However, the above rules do not provide adequate guidance when the characters to fill the spaces are not easily determined. In many scenarios, the spaces / cells in the puzzle require players to fill them through trial and error, and multiple candidate characters may be tried before determining the correct placement of characters in the spaces (for example, in Sudoku, all integers from 1 to 9 may be tried). This scenario should be handled appropriately by a labeling system.

[0079] Some embodiments of the present invention propose addressing label generation in the above scenario, based on the view that the usual goal of a puzzle is to efficiently fill the space and that trial and error is usually inefficient. Due to the effects of trial and error, the process of determining letter labels is often prolonged, resulting in "higher" or "farther" alphabetic letters than, for example, in the step of filling a cell, the label could be found more directly by eliminating unsuitable candidates.

[0080] There can be several meaningful ways to associate a label with a cell that has multiple, not obvious, candidate characters for filling. One example of the selection process involves a labeling mechanism that considers trials with characters that result in failures, i.e., rules, given pre-filled spaces, or spaces that were (correctly) filled in earlier steps of the solution process.

[0081] Therefore, if only two characters are conceivable to fill a cell, one will result in a contradiction, while the other will correctly fill the space. For example, in a step labeled X (assuming Roman letters are used for the labels), if filling the first of the two characters results in a contradiction, the space is filled with the other (second) character, and the label Y (the subsequent label immediately following X in the series of labels) is associated with the filling. This method of label association is consistent with and compatible with associating the first label with the cell filling based only on given rules and pre-filled cells.

[0082] This method means that the correct filling of a space with a character is associated with a label whose placement in the space is ultimately determined by the other character, which is inconsistent. This method expresses the attribute in puzzles (e.g., Sudoku), or more generally, constraint satisfaction problems, that the goal is to eliminate options where the first means of satisfying the constraint cannot work.

[0083] This method of using contradictions to find a suitable label can be extended to cases where there are three or more character options that can fill a cell. This extension is possible by pairing the characters that can fill the cell, breaking them down into fills and associated labels, considering all options in order, and finally finding one of the aforementioned set of labels that fills the cell with characters that do not contradict any preceding fills.

[0084] However, as described in the following paragraphs, if there are three or more options that can fill a cell, the method of searching for an appropriate label using contradictions can be simplified.

[0085] In the solution step, if there are three or more characters that could potentially fill a space, you must use trial and error to find the only number that does not cause any contradictions and fill the cell with that number.

[0086] All numbers that can fill a cell are placed in a List, with a set of labels consisting of the Roman letters {A, B, C, ...}. The List is constructed by excluding numbers that are easily identifiable as being inconsistent with the rules, and other cells are either already filled or have been assigned or filled in during the process up to the current step.

[0087] Assuming that only one number can correctly fill a cell, ultimately all but one number in the List will be inconsistent and removed. The remaining number will correctly fill the cell. The label for filling is then searched based on the other characters in the List, each of which is inconsistent.

[0088] Therefore, to find a label, the process involves (i) tentatively placing candidate characters from the List in the space to be filled, (ii) associating the placement with a tentative label based on a point in the solution process where the cell is filled, (iii) continuing to fill empty spaces and associate labels according to the labeling rule until a contradiction occurs, (iv) noting down the label where a contradiction occurs, (v) if multiple contradictions exist along different paths from the cell to be filled, noting down the label closest to the tentative label, (vi) referring to the noted label as the "first" label associated with the contradiction, (vii) repeating the tentative placement process for each character on the List, (viii) searching for the label furthest from the tentative label among all the "first" labels associated with the contradiction (for multiple candidate characters), (ix) filling the space with a single character where no contradiction is found, and (x) associating the label following the furthest label found at at least one location in the set of labels with the filling.

[0089] As an example, suppose we are at the stage of filling in the cell whose last label in the path is B. We select a number from the List and tentatively link it to the cell associated with label C, then proceed to fill in the other cells. For example, if a contradiction occurs at the stage of label E, we record this fact and then attempt to place the next number in the List. When linking the letter (number) associated with label F, we record this fact again, assuming that the next number in the List is also contradictory. We proceed similarly for all the numbers in the List. L will be the "highest" label for the contradictory number in the List (i.e., it will have the highest ordinal number in the series of labels). Then we associate the filling of this cell with M.

[0090] Note that the "farthest" label is generally the label furthest from the "provisional" label in a set of labels, and in the optimal case, it will be a cell-filling label that "just" exceeds the label associated with any of the contradictions. In the example above, it was implicitly assumed that E and F, etc., were the "first" labels linked to the contradictions. Unless these are the "first" labels, the association of labels with cell filling is not optimal, but not inaccurate. For example, in a competition, players try to select a path to fill empty spaces in order to optimize labeling.

[0091] To systematize this algorithm (and to keep a record), when uppercase letters are used for labels, it is useful to introduce another secondary set that can map to a set of labels associated with a List (of possible characters). In the case of uppercase Roman letters such as labels A, B, C, etc., such readily available secondary character sets are lowercase Roman letters such as a, b, c, etc., and can be used as follows (for example, for Sudoku): In the List of possible numbers for a particular cell, if there are no cells with labels higher than A that would affect filling, the letter "a" is associated with the List; if there are no cells with labels higher than B that would affect filling, the letter "b" is associated with the List, and so on. And if the List is referenced only based on pre-filled cells, no lowercase letters are associated with the List. In this system, uppercase labels can be considered as a primary set of labels.

[0092] Conceptually, in this system, lowercase letters are thought to capture the intermediate state of the puzzle solution at the end of the association with the corresponding uppercase letters A, B, C, etc., which serve as labels for the cells. The list of possible letters and secondary labels is merely a provisional means of determining the actual label associations with A, B, C, etc.

[0093] Here, using an example of a Sudoku puzzle in Figure 29 (with a partially filled state shown in Figure 30), we will explain the process of determining labels for filling the puzzle cells by trial and error using uppercase and lowercase letters. For clarity, Figure 30 shows only label A, which is associated with cell positions (1,2), (1,4), (3,1), (5,6), (7,8), (8,5), (9,2), and (9,3). These are all easily determined by the filled cells and the rules of Sudoku. Some cells also show the word "List," but each cell is filled with three or fewer possible numbers. In Figure 30, for clarity, if the List filling a cell has four or more possible numbers, it is left blank.

[0094] In practice, through trial and error, it's better to continuously update the List of Cell Filling as more cells are filled and labels are assigned, rather than working with the initial List one cell at a time. The lowercase letters associated with the List may change if the List is updated with more information during the solution process.

[0095] Next, we will explain how to use a List, taking cell (1,5) into consideration.

[0096] The list of numbers that can fill the cell at position (1,5) in row 1, column 5 is 4, 7, and 8. If the number 4 is placed in cell (1,5), then the number 5 must be placed in cell (2,5). This is because using any other number from 1 to 9 would inevitably lead to a contradiction with a number already in the second row or fifth column. However, if 5 is in (2,5), there are no numbers from 1 to 9 that can fill the (8,5) position, which would contradict the Sudoku rules. Therefore, 4 cannot be placed in (1,5). Also, if 5 could be placed in (2,5), a contradiction would arise at (8,5) after the association of label A (i.e., as a result) at the beginning of B. If the number 7 is placed in cell (1,5), then 7 cannot be placed in (1,8) or (1,9). However, since 7 is present in (2,2), 7 cannot be placed in (2,9). Therefore, there are no cells in the top right box where 7 can be placed, which contradicts the rules of Sudoku. This contradiction occurs at the stage where label A is associated. Therefore, we need to fill cell (1,5) with 8, which is the only number remaining in the list. Regarding the association of this fill with labels, we examine a list of all possible numbers and the associated labels where inconsistencies occur. In this case, the labels are B and A. Of the series of labels, the label furthest from the others in this list is B. Therefore, cell (1,5) is filled with the number 8 and associated with label C (the label that follows B in the series of labels). If the player chooses to associate label B with filling, this is a form of circular reasoning (associating label B with B), which would be incorrect according to the rules for label association. However, on the other hand, if, for example, the player chooses to associate label D with this filling for computational safety, that would be acceptable. Label D for filling cell (1,5) does not violate the labeling rules, but because label C is appropriate, it may negatively impact the efficiency measure of the player's solution path.

[0097] It is important to note that even if the same cell is filled with the same characters, different labels can be considered part of different solution paths. This is because these can affect the association of labels further down in different space-filling processes.

[0098] In reality, exploring all label associations through trial and error is extremely difficult. Generally, it is more practical to directly fill and associate cells with appropriate labels as much as possible through constraints and / or observation, and then fill and associate the remaining few empty cells with labels through trial and error. However, a skilled player may be able to figure out a clever and quick way to remove characters from the List and explain it logically.

[0099] Figure 31 shows the solution to the puzzle in Figure 29, with the blank cells filled with the numbers 1 through 9. It also shows a list of some cells at different points in the solution process where lowercase letters are used when the labels associated with cell filling are uppercase. Figure 31 also shows the logical reasoning behind the use of the exemplary icons shown below in this specification. These icons, along with the order in which the cells are filled in the solution process, can help convey the logic the player used to fill the cells. This logic may be used by a computer system to verify cell filling and associated labels, or by a competition administrator, for example, to accept or separate solution paths.

[0100] In this simple puzzle, we can see that the labels shown in Figure 31 are not necessarily the "lowest" possible letters for every cell. For example, the label for cell (7,4) is entered as "D," but a more attentive player would notice that "C" is also possible. We can say that D is incorrect because it does not violate the label association rules, but it is not optimal. Ideally, each cell would be filled in such a way that the measure of efficiency is optimized.

[0101] Optimizing the efficiency measure of a puzzle generally cannot be determined from the initial data without understanding at least some of the possible solutions. This is generally true for all methods of evaluating the "difficulty" of a puzzle or constraint satisfaction problem and similar descriptors. Label association and efficiency measure calculations are additional means of estimating the difficulty of a puzzle.

[0102] Checking the labels associated with the solution steps. The association of labels for filling in puzzle cells needs to be verified because it affects real-world practicality, regardless of how the labels are searched.

[0103] Label association verification is best performed by computer systems. The process is too time-consuming and prone to errors when done manually. More importantly, for multiple real-world scenarios (e.g., selecting winners in a competition), computer execution with appropriate features and safeguards is preferable to ensure the privacy, independence, security, and integrity of the verification process.

[0104] To verify label associations, adherence to label association rules is required. For example, a cell associated with the label "C" (when uppercase Roman letters are used as labels) should not be filled, but instead be labeled based on another cell associated with a letter after C. If a path or answer segment provided by a player has an incorrect label associated with it, that path may be removed, separated, or excluded for separate processing by the administrator of the organization convening the activity or competition before it can be used for its intended purpose.

[0105] The puzzle shown in Figure 10, and the solutions shown in Figures 11, 12, and 13, demonstrate how the puzzle cells, when filled in in different orders, can pique the interest of elementary school students in numerical facts and their respective mathematical relationships.

[0106] Using the puzzle in Figure 10, we illustrate a new method for generating hints for current continuing-part applications.

[0107] Instead of selecting one or more known solutions to generate hints for solving the puzzle, the system may be configured to generate all possible combinations of solutions presented. For example, in Figures 11, 12, and 13, cells (1,2), (1,3), (2,1), (2,3), (3,1), (3,2), and (3,3) are given the labels C / C / D, D / D / E, E / D / E, E / E / E, D / C / D, B / B / C, and C / A / B, respectively.

[0108] Labels A, B, C, D, and E can be combined by assigning them values ​​1, 2, 3, 4, and 5. For example, combining the labels as averages for each cell results in values ​​of 2, 2.33333, 3.33333, 3.66666, 4.33333, 4.66666, and 5 for the same cell. Other algorithms exist for combining values / labels.

[0109] Based on these calculations, a new "integrated label" can be found. For example, the above average can be converted to the "closest" label as B, B, C, D, D, E, and E. This gives new players a good idea of ​​which cell to tackle first, which cell to tackle second, etc.

[0110] Furthermore, in more complex puzzles (beyond this elementary puzzle), more sophisticated methods can be used to combine labels and generate integrated labels. By generating partitions of calculated combined values, the optimal number of hints can be assigned to the target audience. For example, one might want to give only three hints to the KenKen puzzle in Figure 10. In this case, a decision to determine the partitions can be made (by a human instructor or a programmed machine). For example, the average of the first three values ​​might correspond to A, the next two values ​​to B, and the last two values ​​to C.

[0111] Such methods can be effectively used for complex problems by using computer-generated composite values ​​and labels that can be determined more "objectively" and stabilized.

[0112] The method using integrated labels is particularly useful for generating hints to solve puzzles. Since the hints are intended to assist human players, this approach combines input from multiple human players and processes it using a computer.

[0113] In one embodiment, the baseline flow for generating labels and hints is shown in Figure 24. This flow can be suitably adapted to other algorithms for combining labels.

[0114] When used to generate labels and hints, computers typically verify not only that cells are correctly filled with numbers or other characters, but also that the labeling of the cell filling is correct. This verification process is shown in Figure 25. The process for generating integrated labels is shown in Figure 26.

[0115] The association of the "correct" label has a meaning corresponding to, or similar to, the following paragraphs.

[0116] Given a set of labels, any cell in a puzzle filled based on a given rule and only an arbitrary given number of non-empty (pre-filled) cells is associated with the first label, and any cell filled based on a given rule, pre-filled cells, and the cell associated with the first label is associated with the second label, and so on.

[0117] Computer-based verification ensures that, for example, a cell associated with the label "C" does not require another cell associated with the label "C or greater". If a path or solution segment provided by the player contains incorrect labels, that path will be removed before the labels are combined to generate a unified label or hint.

[0118] When generating labels for filling cells through trial and error, this can be addressed by keeping in mind that if the characters to fill the cells cannot be easily and clearly determined, it will be necessary to try different characters to fill the spaces. If the goal of the puzzle is to efficiently fill the spaces (a reasonable assumption), then as trial and error prolongs the character determination process, the resulting labels will be more "distant" from the set of labels associated with the cell-filling steps.

[0119] There may be several meaningful ways to associate a label with a cell that has multiple candidate characters for filling. One process selected in this application is to estimate the length of the decision by considering trials with characters that fail, i.e., rules, given pre-filled spaces, or characters that result in outcomes inconsistent with spaces filled in previous steps of solving the puzzle.

[0120] Therefore, if only two characters are conceivable to fill a cell, one will be inconsistent, and the other will be correctly placed in the space. (Assuming that spaces are filled with numbers and labels use Roman letters) For example, if an inconsistency occurs in step X, the correctly filled character will be associated with label Y (above X). This method of label association is compatible with associating the first label with cell filling based only on given rules and pre-filled cells.

[0121] If there are multiple characters that can fill a cell or space, the above procedure can be extended by pairing possible characters and breaking down the cell fill and associated label.

[0122] Figures 3 and 4 illustrate the label association process when a trial-and-error approach is required.

[0123] To illustrate the structure and algorithm of the key ideas disclosed in this invention, we begin with a simple example of a logic puzzle known as "KenKen," which has rapidly gained popularity. Unlike Sudoku, solving the KenKen puzzle requires not only an understanding of numbers but also a grasp of simple arithmetic operations.

[0124] Similar to Sudoku, KenKen has a grid of cells arranged in a matrix that can be filled according to the rules listed below.

[0125] Rules 1, 2, and 3 combined mean that if the number of rows and columns is n, then all numbers from 1 to n are used exactly once to fill the grid. Puzzles where the number of rows or columns are not equal, and row index i is from 1 to m and column index is from 1 to n (n ≠ m), are also possible, but these possibilities will be ignored in this discussion.

[0126] Rules 1, 2, and 3 above apply to many logic puzzles (including Sudoku and KenKen). Rule 3 describes the following important practical point for puzzles of interest: filling spaces or cells is a definitive action, but determining which numbers cannot be used to fill cells is a truly investigative act.

[0127] Furthermore, Rules 1, 2, and 3 imply the following duality regarding the filling of spaces with characters: if all but one character is removed from a space, the single remaining character fills that space; and if all but one space in a row or column is removed from a particular character, that character goes into the single remaining space.

[0128] However, unlike Sudoku, where the number of rows and columns of boxes (blocks) are usually equal, KenKen's boxes, also called cages, can be uneven or irregular in shape. Also, unlike Sudoku, filling the cells with numbers involves arithmetic operations. The cells of the KenKen puzzle are organized as irregularly shaped cages (boxes), so that the numbers within a cage can produce a given result through a given arithmetic operation specified for each cage. As a result of this layout, unlike Sudoku, KenKen numbers are repeatable within a cage / box, unless a repeat occurs within a row or column.

[0129] We assume that the puzzles of interest have a unique final solution, that is, that all spaces in the correctly filled grid are identical.

[0130] Generally, even if the sequence of steps from start to finish results in the same unique and correctly filled grid, we will distinguish between the "solutions" presented by the players or multiple attempts by the same player. As mentioned above in the overview section, a set of steps in a solution process executed in a different order may have different desirable states depending on the logical conciseness and directness of each step. For example, a simple way to distinguish the order of steps in solving a puzzle from another order is to prefer a direct and compact process over a puzzle-solving process that may continue for a long time. Example: KenKen puzzle, effect of the order in which cells are filled, and quantification of the effect.

[0131] To obtain an essential measure of the solution to a puzzle, game, or activity, we calculate a "measure of efficiency" of the path or sequence of steps, which is determined by the order in which the steps are performed or the order in which the puzzle spaces or cells are filled. This is illustrated with an example of a "simple" KenKen puzzle, where the difference due to the order in which the steps are performed can be defined and quantified.

[0132] The key points of this method are illustrated by the puzzle in Figure 10 and the three solutions presented in Figures 11, 12, and 13. The puzzle in Figure 10 is a KenKen puzzle, which shares some similarities with Sudoku but has several important differences.

[0133] By examining the simple KenKen puzzle shown in Figure 10 in detail, we demonstrate a method that not only distinguishes "solutions" based on the order in which the puzzle is solved, but also quantifies the differences.

[0134] The KenKen puzzle in Figure 10 is very simple, consisting of a 3x3 grid of cells and five cages (i.e., boxes) indicated by thick outlines. The only arithmetic operation involved is addition, as each cage / box contains either a number or a number with a plus sign "+". A cage containing only a number consists of one cell in the grid and will therefore be filled with that given number. A cage containing both a number and a plus sign indicates that the numbers filled in the cells within that cage will sum to the specified result.

[0135] According to standard matrix notation, the cells are represented as (1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), and (3,3) according to their respective positions in the grid, where (i,j) represents the cell position in row i and column j in the grid. The puzzle is solved when each cell in the grid is filled with a number according to the rules.

[0136] Figure 10 shows that there are nine cells and five cages: (1,1), (2,2), (1,2)(1,3)(2,3), (2,1)(3,1), and (3,2)(3,3), and that the solution can be written as follows: cell (1,1) = cell (2,2) = 1, (2,1) + (3,1) = 5, (3,2) + (3,3) = 3, and (1,2) + (1,3) + (2,3) = 8 (assuming that the numbers in two cells are known from the start, and seven cells need to be filled in by the player).

[0137] Furthermore, since this puzzle is a 3x3 grid, Rules 1, 2, and 3 imply that each cell is filled with one of a set of numbers 1, 2, and 3. In the following explanation of the solution, the numbers to be filled in the cells are indicated by the symbol "=".

[0138] The first solution to the puzzle in Figure 10 (shown in Figure 11) To solve this puzzle, we will fill in the cells by reasoning as follows.

[0139] First, considering a cage whose sum must be 3, the only possible sums are 2 and 1. Therefore, cells (3,2) and (3,3) can be filled with the numbers 1 or 2, respectively. Since (2,1)=1, by Rule 2, (3,2)≠1. Thus, (3,2)=2, which implies (3,3)=1.

[0140] After that, there is only one cell left that is not filled in row 3 (i.e., (3,1)), and according to Rule 3, it needs to be filled with the only remaining unused number (i.e., 3).

[0141] Next, moving to the first column, the only cell that remains unfilled is (2,1), and according to Rule 3, it must be filled with the only remaining number (i.e., 2).

[0142] Next, looking at the second row and second column, there is one empty cell remaining in each (i.e., (2,3) and (1,2)). These cells will each be filled with the only remaining number, 3.

[0143] Finally, fill the last empty cell with the only number that is still not present in the first row and third column (i.e., 2).

[0144] Thus, the cells in the answer are filled in the following order: (3,2), (3,3), (3,1), {(2,1), (1,2)}, (2,3), (1,3). The brackets {} indicate that the order in which the cells enclosed in brackets {} are filled is not important.

[0145] To solve this puzzle, you must rely on the basic rules Rule 1, 2, and 3 mentioned above, which stipulate that no number is repeated in any row or column, and that all numbers from 1 to 3 are used exactly once in each row or column.

[0146] Quantification of the logical progression of the solution The next step in quantifying the logical order in which steps in an activity, game, or puzzle are performed is to associate these steps with numerical values. However, quantifying the logical order requires providing a concise logical structure or algorithm for tracking the order in which the steps of the activity are performed.

[0147] In the case of the puzzle in Figure 10, the activity step is "Fill in the 'empty' cells."

[0148] By associating each step of filling in cells with a label, the order in which cells are filled can be tracked. Labels are sets of letters that have a predetermined or natural partial order that meaningfully describes the “order” or execution order of the steps. The Roman letters A, B, C, ... or the set of integers 1, 2, 3, ... are readily available sets of letters that make sense in terms such as “order,” “preceding,” or “succeeding.” For this reason, these sets of letters can be used as labels for the steps of an activity. However, to avoid confusion, it is preferable to use the letters A, B, C, ... for puzzles where cells are filled with numbers (e.g., Sudoku), and sets of integers as labels for puzzles where cells are filled with letters, such as Word Sudoku.

[0149] It is important to note that the labels associated with the cell-filling steps will not be unique. In fact, since cell filling is determined by the order in which the cells are filled, one should not expect the labels of the activity steps to be unique. What is required of the labeling algorithm is to provide instructions to associate at least one label with each cell-filling step.

[0150] One algorithm for setting up labeling One algorithm for setting up labeling can be configured as follows:

[0151] First, note that a partial order can be induced by Roman characters.

[0152] Thus, when the cell number is directly determined based only on the basic rules and the numbers given at the start of the puzzle (e.g., in a 1-cell cage of KenKen), the character A is associated with the cell. If the filling is based on the basic rules, the information given at the start of the puzzle, and at least one cell associated with A, but not based on any cell associated with a character "higher" than A (i.e., the characters following Roman A), then the character B is associated with the cell. If the filling is based on at least one cell associated with B, but not based on any cell associated with a character C or higher, then the character label C is associated with the cell, and so on.

[0153] Generally, similarly, using the usual order of the letters of the alphabet, when the filling is based on at least one cell associated with the immediately preceding letter in the alphabet, but not based on any cell associated with a "higher" letter, the letter of the alphabet is associated with the filling of the cell. Thus, A < B < C < ···, and subsequent letters can be considered "higher" than preceding letters.

[0154] Labels A, B, C, ···, as follows, by the method of associating this character label with the cell, extend the basic rules for solving the puzzle, and in any solution of the puzzle, provide a workable mechanism for the order of filling the cells Track for.

[0155] Rule 4: When the filling of a cell is at least partially based on one or more cells associated with the immediately preceding letter of the alphabet, but not based on any cell associated with a letter that does not precede the selected letter, associate the filling with the cell using the said letter of the alphabet as a label.

[0156] Figure 11 shows the filling of the KenKen puzzle grid in Figure 10 in the order described above. Here, we first infer that (3,2) is either 1 or 2, and (3,3) is either 1 or 2. In this inference, neither of these two cells can be filled, and the only direct dependencies are the given numbers and Rules 1 and 2. To determine the numbers that can be filled in (3,2) and (3,3), we need to use other information (for example, (3,2) cannot be filled with 2). Therefore, according to Rule 3, neither of these two cells can be labeled A. However, (3,2) cannot be filled with 1 because this would contradict Rule 2 and the number 1 in cell (2,2). Thus, by a "one-step" logical inference, cell (3,2) is filled with 2. Also, Rule 3 associates the filling of cell (3,2) with the following label B.

[0157] Next, fill the following cell (3,3) with 1 and associate label C with the cell filling.

[0158] The filling and labeling of cells (3,2) and (3,3) are shown in Figure 22.

[0159] By similar reasoning, the filling of cell (3,1) is associated with D, the filling of (2,1) is associated with E, and the fillings of (1,2), (1,3), and (2,3) are associated with C, D, and E, respectively.

[0160] Next, we consider the solution to the same problem, but the cells are filled in a slightly different order, as shown in Figure 12.

[0161] Solution to Figure 12 Given that the order in which cells are handled in Figure 12 is given as (1,1)=1 and (2,2)=1, we begin with the view that Rule 1 means that the number 1 cannot be placed in any other cell in either the first or second row, and Rule 2 means that 1 cannot be placed in any other cell in either the first or second column. Therefore, according to Rules 1, 2, and 3, the only cell that can be filled with the number 1 is the third row, third column, i.e., (3,3). This filling is directly determined by applying Rules 1, 2, and 3, as well as the given numbers (to the cage of one cell), so we associate A with (3,3)=1.

[0162] However, since (3,2)+(3,3)=3, (3,2)=2, so the letter B is associated with filling cell (3,2). Figure 23 shows the logic of this labeling.

[0163] Subsequently, (3,1)=3 is associated with C. This implies (2,1)=5-3=2, which is then associated with the next letter, D. This filling is confirmed by using at least one cell associated with C.

[0164] Then, since the other two cells in the second column, namely (2,2) and (3,2), are 1 and 2 respectively, (1,2)=3, so C is assigned. As a result, (1,3)=2, so D, and finally (2,3)=3, so E. This is the solution shown in Figure 12.

[0165] Figure 13 shows yet another solution, namely, a different order for filling in the cells.

[0166] This example demonstrates the following important facts when comparing "solutions" to a puzzle or activity obtained by performing the steps in a different order:

[0167] Labels such as alphabetic letters or integers, when used in this context, are devices and structures that encapsulate the logical progression of the solution, and despite their familiarity, they are not used in their usual linguistic role.

[0168] Comparison of the solutions in Figures 11, 12, and 13 To compare the solutions in Figures 11, 12, and 13, the following reasonable assumptions can be made.

[0169] Assumption: The shorter the sequence of labels A, B, C, ... used in solving the puzzle, the more "efficient" the puzzle solution becomes.

[0170] According to this assumption, Figure 11 has one B, two Cs, two Ds, and two Es, while the solution order in Figure 12 has one A, one B, two Cs, two Ds, and one E. Therefore, the solution order in Figure 12 can be considered slightly more efficient than the solution order in Figure 11.

[0171] Furthermore, to facilitate comparison, numerical values ​​may be associated with text labels. That is, 1 is associated with each A, 2 with each B, 3 with each C, and so on.

[0172] By assigning numerical values ​​to labels, it becomes possible to obtain a single number that captures, for example, the logic of a solution obtained in a specific order. In addition to using the number of cells / spaces filled in this process toward the puzzle solution, a weighted "average" value associated with the solution or its segments can be calculated by assigning numerical values ​​1, 2, 3, ... to labels A, B, C, etc., and using the frequency of occurrence of these labels as weights. This weighted average is a normalized value that can also be interpreted as a value associated with the "normal" filling of empty cells in the puzzle during the solution process. A larger average value indicates a longer solution, while a smaller value indicates a more efficient solution.

[0173] In the case of Figure 11, the weighted average is (2*l + 2*3 + 2*4 + 2*5) / 7 = 3.7142 (rounded to the fifth decimal place).

[0174] In the case of Figure 12, the weighted average is (l* 1 + 2* l + 2* 3 + 2* 4 + l* 5) / 7 = 3.1428.

[0175] Therefore, it can be concluded that Figure 12 shows a more "efficient" solution.

[0176] Figure 13 shows the third solution to the same problem, which contains one B, one C, two Ds, and three Es. The average value of this solution is 4.0, which is less efficient than the other solutions. Quantifying and comparing the logical order in which activity steps are performed.

[0177] This example demonstrates that (1) even if the completed solution is unique, the order in which the cells of the puzzle grid are filled is important, and (2) cell filling can be logically quantified, and the logical difference between two different cell filling orders can be captured in a practical and meaningful manner that does not depend on the time taken to solve the puzzle as a measurement parameter.

[0178] Furthermore, assigning numerical labels allows us to assign numerical values ​​to segments of puzzle solutions within a given class. Thus, comparisons between solutions or between solution segments become as straightforward as comparisons of real numbers. The method and construction presented here are extendable to a wide range of activities, games, and puzzles. The comparative possibilities based on the method and construction illustrated in this KenKen puzzle prove invaluable for creating new competitive games and activities based on known implementation activities. However, extending this method and construction to activities other than puzzles requires the explanations and definitions outlined in the following paragraphs.

[0179] In the following explanation, this method extends beyond Sudoku, KenKen, crosswords, etc., to activities that can be performed step by step. In these activities, "filling in letters" into the grid spaces or cells may not seem directly meaningful, but the "linking letters" to the steps may have a similar meaning to filling in cells in Sudoku, etc.

[0180] The methods disclosed herein are applicable to activities that comprise the execution of a series of steps from an initial state defined as the start of an activity to a final state defined as the end of an activity, in accordance with a set of instructions for determining one or more steps that can follow the steps of the activity during the execution of the activity, wherein the steps of the activity are associated with calculated measurable quantities.

[0181] Furthermore, by using a pre-configured algorithm, measurable quantities may be calculated and associated with one or more sets of steps in an activity. This allows the measurable quantities to be associated with completed activities or segments thereof. The purpose of associating these measurable quantities with activity steps as much as possible is to compare two or more different sequences of performing the activity steps and select a preferred sequence. These measurable quantities may be referred to as a "measure of efficiency" in performing the associated sequence of steps.

[0182] In some embodiments, the method described herein comprises: (1) providing an algorithm or mechanism for tracking the order in which the steps of an activity are typically performed toward a goal of completing the activity; (2) associating each step of the activity with a quantity (e.g., a real number) that takes into account the order in which the steps are performed; (3) combining the quantities associated with a set of steps as a single measure; (4) comparing two or more sets of steps based on the respective measures obtained in the combining step; and (5) ranking two or more sets of steps by the order derived from the comparison of the respective numerical measures.

[0183] Naturally, the activity may be any suitable activity that can be performed in steps following two or more different sequences. The quantities associated with the steps of the activity may be suitable numerical values ​​recognized in an arithmetic formula for calculating a single measure of the sequence. Furthermore, the quantities associated with all the steps in the sequence in which the steps of the activity are performed may be suitably and practically combined.

[0184] In some embodiments, the results of the ranking may be presented on a suitable tangible medium. The tangible medium may include, for example, printed publications, game boards, computer equipment, televisions, tablets, mobile devices (e.g., mobile phones, smartphones, PDAs), and any other suitable medium. The ranking results may be presented after being transmitted to a suitable device or other means via a computer network, the internet, or any other method. A tangible game board may include a set of given letters, a set of labels, and a set of logical reasons and algorithms as tangible game pieces.

[0185] A key subclass of activities of interest involves activities that, given a set of spaces that are at least partially empty and a set of different characters, link one of the characters from the set to each empty space in the set of different spaces using a given set of rules for linking characters to spaces.

[0186] The sequence of steps in such activities does not necessarily involve a continuum like rows or columns of a grid. The "continuity" between spaces linked to characters is maintained by the logical relationships between the spaces linked to the characters.

[0187] Therefore, for such an activity, one or more spaces in a set of spaces may have one or more linked characters at the start of the activity, a character is linked to each of the designated spaces in the set of spaces at the end of the activity, an empty space is a space without linked characters, a space with linked characters is not empty, a set of spaces has at least one empty space at the start of the activity, and the Step of the activity does not contradict any of the aforementioned set of rules and does not contradict any link of characters to the spaces given at the start of the activity. It can be specified that there is a link to one of the set of characters for any empty space; that a causally connected pair of steps is a pair of steps in which the result step follows the cause step by the execution of the set of rules; that a connected series of steps is a series of causally connected pairs of steps, the first of which is the cause step, each subsequent step except the last step of the connection being a result step and a cause step, the last step of the connection being the result step, and the series of steps having at least one connection being a path or a segment thereof; and that a measurable quantity called a measure of efficiency of the path or segment thereof can be calculated. Such activities can be concisely described by the assumption that a set of distinct characters is {Char(1),Char(2),···,Char(I),···Char(λ)} (identified collectively as {CHARS}), a set of spaces is {Space(1),Space(2),···,Space(I),···Space(σ)} (identified collectively as {SPACES}), and a set of rules is {Rule(1),Rule(2),···,Rule(I),···Rule(ρ)} (identified collectively as {RULES}), and a measure of efficiency can be calculated.

[0188] A measure of the efficiency of a path or a series of steps can be calculated by assigning numerical values ​​to labels associated with character links to spaces. For integers J and K (1 ≤ J ≤ λ and 1 ≤ K ≤ σ), the link of character Char(J) to Space(K) includes an association with the link of Label(I), where Label(I) belongs to a set of labels ({LABELS}={Label(l),Label(2),···,Label(I),···}), and (a) if the link is consistent with a given link of {CHARS} to {SPACES} at the start of the activity, then Label(1) is associated with character Char(J) and space S If Label(I) is linked to space(K) and (b) the link is consistent with the associations of Label(1), Label(2), ..., Label(L1) with (i) a Rule from the set {RULES}, (ii) a given link of {CHARS} to {SPACES} at the start of the activity, or (iii) a link of the character {CHARS} to a space other than Space(K), then Label(I) is associated with the character Char(J) and linked to space(K).

[0189] For activities that conform to the above description and the method of tracking the execution order of steps by labeling, the calculation of a measure of efficiency can be achieved by providing (1) an algorithm for assigning numerical values ​​to labels and (2) an expression for combining numerical values. This method is described and illustrated in detail below.

[0190] Uses of the method Multiple interesting embodiments are possible and are included in the spirit of the present invention, such as variations of basic puzzles, novel methods to assist players, use in education and data security, artistic expression in various forms, and live or televised competitions.

[0191] Variations of basic puzzles In one conceivable embodiment of the present invention, it is possible to have multiple players compete against each other. By using the path each player takes to reach the solution in this manner, an "efficiency" score is generated, which is a measure of the efficiency of each player's path to the solution. The player with the highest score wins.

[0192] In one variation of this embodiment, a single player can calculate their score for a particular puzzle and compare it to the highest possible score. This can provide the player with insights into how to improve their solving strategy. It also allows them to try and achieve more efficient scores over multiple attempts at the same puzzle. Activities involving chance

[0193] As described above, the method of this disclosure can be used for a specific class of games and activities, in addition to the element of chance. By using labels such as A, B, C, etc., to which numerical values ​​are assigned, the efficiency score of a series of steps and segments of the path to the "solution" can be calculated. For this reason, the use of labeling can, for example, represent the most efficient row, column, or box in a Sudoku puzzle, which can be called the first row, column, or box to be filled in.

[0194] This could allow live or remote audiences of a Sudoku puzzle competition to bet on the first row, column, or box to be filled. Other possibilities for audience participation include betting on one or more winning players, the shortest solution, the best estimate of difficulty, the number of cells labeled A, B, C, etc. As with these examples, many other variations of the above use can be generated by using methods of labeling the path to the solution or its segments, or a specific set of steps.

[0195] New ways to assist players One application of the present invention is a method for providing hints for solving Sudoku puzzles or similar problems. For many such problems, hints tend to be ad-hoc, as they depend on the real-time state of the puzzle board as it progresses. Therefore, hints are usually limited and cannot be used for problem sets that are not typically presented in electronic form.

[0196] Therefore, for example, when trying to solve a puzzle online and requesting a hint at a specific stage of a Sudoku problem, some other systems currently available can provide a form of hint by marking the next cell where the player can fill in letters, based on the cells the player has already filled in. However, this method of dynamically providing hints at runtime is merely a stopgap measure and cannot be used a priori. For example, if the puzzle is printed in a book or newspaper, the complete solution, if available, can only be considered the sole hint.

[0197] On the other hand, according to embodiments of the present invention, hints for each puzzle can be generated a priori, making them available to players who need hints to solve the puzzles but seek the enjoyment of solving them without referring to the entire solution. These hints can be published in static media such as books and newspapers. Similarly, various forms of systematic dynamic hints can be made available for electronic or real-time solving actions.

[0198] The method described in the claims may be used in the development of a system for providing a player with extensive hints for solving a puzzle. Thus, even if a player attempts to solve the puzzle and gets stuck and loses their way, they do not need to look at all the solutions to fill in the troublesome cells or give up in despair.

[0199] This invention enables a clever method for assistance. If a player gets stuck, this method can be used to display, for example, all spaces that are one step away from a filled space. For example, at the start of the puzzle, several of the spaces are already filled. If the player requests a hint at that point, this method can also highlight all spaces that can be determined based solely on a given number.

[0200] In one modified version of this embodiment, the puzzle spaces may be marked with hints from the outset, indicating at what stage of the solution process the player is expected to fill in each space. For example, spaces that can be filled in at a given stage may be marked in red, while spaces that can be filled in at a different stage may be marked in blue. This embodiment can be useful for both beginner players learning how to play and experienced players seeking to further improve their skills.

[0201] In another variation of this embodiment, the puzzle may be displayed on one page or screen, a puzzle with hints may be displayed on another page or screen as needed, and finally the entire solution may be displayed on yet another page or screen. For players who are stuck at an intermediate point in the solution, it may be sufficient for them to look at the hints (e.g., color-coded hints) and focus their attention on the path forward. This method provides the player with a path forward while maintaining the challenge, enjoyment, or entertainment value of the puzzle activity.

[0202] In another variation, the difficulty level of the puzzle may be indicated, which may be superior to the conventional "number of stars" currently used by many newspaper columns, books, and other publications to indicate the difficulty of a puzzle. Based on relatively "efficient" solutions, such an estimate of difficulty may be given as a bar graph, indicating not only the difficulty level of the puzzle but also the point at which it is expected to become more difficult.

[0203] Figures 16, 17, 20, and 21 are bar graphs of solutions 15 and 19 for each Sudoku puzzle. An interesting fact that emerges from calculating the efficiency measures of the two puzzles is that the puzzle with 27 numbers pre-filled is more difficult than the puzzle with 24 numbers given. Furthermore, by comparing the efficiency measures of each, it is possible to quantitatively estimate how much more difficult the problem in Figure 18 is than the problem in Figure 14.

[0204] Non-visual methods to assist the player In a potential embodiment, the highlighted spaces do not need to be limited to color coding or visual hints. In an appropriate medium, sound, animation, or video can also be used as hints. This allows for hints that do not reveal too much of the solution, thus not diminishing the enjoyment of solving the puzzle. For example, if the player gets stuck at a particular point, they can choose to leave the space blank. In the method according to the claims, after determining the step to which the space can be filled, a sound clearly associated with that step level is played to distinguish each digit by a different sound, which is somewhat similar to the sound or pitch of a telephone associated with dialing a number.

[0205] Furthermore, similar to the coloring of visual hints, sound hints can be predetermined and communicated to the player at any point in the puzzle-solving process (including the start) when the player clicks on a specific cell.

[0206] Use in education This invention uses an intuitive and engaging method for conveying the logical connections between steps in solving a game that incorporates the identification and reinforcement of puzzles or rules. Therefore, the path to the solution demonstrated by the method of this invention can be valuable in the study, education, and communication of logical analysis and reasoning.

[0207] Artistic expression The method described in the claims can also be used to provide creative insights into the structure of individual puzzles themselves. When dividing spaces to be filled at different stages of the process, the method described in the claims can identify spaces by layers grouped by points where these different spaces can be filled. Alternatively, it may be possible to group specific spaces, connected by logical connections that allow players to fill spaces that are related in a chain or tree structure, as a sequence or "path".

[0208] Structures produced by methods described in such patent claims have many potential applications. By visually representing the structure, it becomes possible to simply place and compare two separate puzzles side by side, or combine them to create overlays. More creatively, it is also possible to use the visual representation of the structure as the basis for paintings or other works of art.

[0209] By using puzzle labels, unique representations can be generated. Labels add another dimension to the numbers, filling the cells of a puzzle grid with numbers, similar to Sudoku. This additional dimension can be used to generate an interesting 3D model of the solution. For example, labels may be distinguished by color, or the numbers placed in the grid of the 3D model of the solution may be distinguished by column height. Alternatively, the numbers in the grid may be distinguished by color, or the column height may correlate with the labels (higher columns representing "higher" labels).

[0210] Those skilled in the art will naturally be able to implement other variations of this method for generating models.

[0211] A suitable visual representation of the puzzle can also be used as the basis for a choreographed dance performance, where steps are creatively harmonized to match the path or stage of each puzzle.

[0212] Another creative use of puzzle structures is their role as a foundation for music.

[0213] Although music is created through artistic expression, it possesses many structural elements. For example, the key of a written piece, its time signature, or the various chords within a song.

[0214] The structure of a puzzle can also be used as the basis for other structures, which in turn makes it possible to generate or compose music unique to each individual puzzle. The pieces of a typical Sudoku puzzle are determined, for example, by a creative interpretation of the dimensions corresponding to the numbers, the labels, and the relative arrangement of the cells filled with both.

[0215] Many of the conceivable applications of these described technologies can be incorporated into television programs featuring all of the above-mentioned aspects. Competitors attempt to complete puzzles, and the efficiency of each solution is judged. During, between, or at the end of these competitions, composers and dancers may also attempt to create unique songs and dances based on individual puzzles. Judges may evaluate participants based on criteria such as adherence to the puzzle structure, aesthetic value, and the relative efficiency of their solutions.

[0216] As described above, the techniques described can be employed in many applications. An example of using these techniques in the game of Sudoku will be discussed later. The processes of other puzzles, games, or activities can be similarly described by appropriately defining the start and goal, providing instructions for moving from one step of the activity to the next (or any of the following steps), and suitably defining the stages or similarities of the stages in which the activity is performed.

[0217] Tracking the process of answering or completing an activity In the case of a typical Sudoku, this method may proceed as follows: (1) Record the order in which cells are filled by the numbers 1-9, associating the stage in which each cell is filled with a letter A, B, C, etc., to represent the stages and order in which empty cells are filled; (2) Assign numerical values ​​to each of the letters A, B, C, etc.; (3) Search for a weighted average of the solutions when performed in the exact order in which the cells are filled, as a measure of the specific path to the solution, based on the number of cells with labels A, B, C, etc. and the numerical values ​​assigned to them; (4) Compare two or more solutions (paths) according to their respective measures; and (5) Rank the solutions in order according to their respective measures.

[0218] In this method, two Sudoku solutions that look very similar but have different preferences or desired states can be identified by associating their order with the order of the real numbers.

[0219] Furthermore, as another simple application, a method based on the present invention can provide a more accurate measure of the difficulty of a puzzle, unlike the currently popular method of evaluating difficulty by the number of "stars" or similar icons. For example, if a skilled Sudoku player can arrive at the best solution with an efficiency scale of 6.9 (assuming that difficulty increases as the efficiency scale increases), then by estimating the upper limit of the scale, it would be reasonable to estimate the difficulty as 7.

[0220] Detailed explanation of the method I will explain this method in more detail below using Sudoku as an example, but it can also be applied to a wider range of situations.

[0221] For example, in a given puzzle, a cell that can only be filled with the number 1 because placing any other number would be inconsistent with at least one other rule or at least one other cell that is filled at the start is linked to A. Similarly, a cell that can only be filled with the number 3 because placing any other number would be inconsistent with another cell linked to a rule or the letter A is filled with 3 and linked to label B, and so on.

[0222] However, for cells where the letter link cannot be immediately determined, it is useful to go through the Listing Step, which allows you to construct a list of all possible numbers for that cell by excluding numbers that contradict the rules or other cells that have already been filled and linked to letters in sets A, B, C, ... from consideration. As with typical trial-and-error methods, it is possible to try placing the numbers in the list one by one.

[0223] Assuming that only one number can be correctly placed in a cell, ultimately all but one number in the List will be contradictory. Therefore, all but one number in the List can be removed, and the remaining number can be placed in the cell. The determination of the label for filling that cell is unclear.

[0224] In such cases, the method for determining the label with the character linked to this cell is obtained algorithmically, as explained in the following example. That is, if the other "playing" cells for determining the character of the target empty cell (besides the fill cell given at the start) are only associated with label B or A, and a List is referenced for the empty cell to be filled, then a number is selected from the List and tentatively linked to the cell associated with label C, and the process proceeds to fill the other cells. For example, if a contradiction occurs at the label E stage, this fact is recorded, and then the placement of the next number in the List is attempted. At the stage of linking the character associated with label F, this fact is again recorded as the next number in the List is also contradictory. The process is carried out similarly for all numbers in the List. L is assumed to be the "highest" label (i.e., the one with the highest ordinal number in the series of labels) for the contradictory numbers in the List. Then, this cell is linked to M.

[0225] To record and systematize this algorithm, it is useful to introduce another set of characters that can be mapped to a set of labels such as A, B, C, etc., and associate these with a List. Such a set of characters could be lowercase Roman letters a, b, c, etc., and can be used as follows: When a List of possible numbers is quoted for a particular cell, if there are no cells with labels higher than A that are currently in play, the character "a" is associated with the List; if there are no cells with labels higher than B, the character "b" is associated with the List, and so on. Furthermore, when the List is quoted based only on pre-filled cells, no lowercase character is associated with the List.

[0226] Lowercase letters a, b, c, etc., are naturally mapped to uppercase letters A, B, C, etc., and are therefore useful as a secondary set associated with a list of possible numbers in an empty cell. In this scheme, lowercase letters can capture an intermediate state ("snapshot") of the puzzle solution at the end of the association with the cell as a label for the corresponding uppercase letter A, B, C, etc. The association of letters A, B, C, etc. in this scheme is considered to occur at the beginning of the association stage (A, B, or C, etc.) of filling the cell.

[0227] Figures 2, 4, 7-9, 11-13, 15, and 19 provide examples of these algorithms, with Figure 4 showing an example of using a list of characters. These show labels such as A, B, C, etc. to the right of numbers placed in cells, and, where necessary, the characters a, b, c, etc., together with the corresponding lists shown elsewhere in the cells.

[0228] The following explanation concerns these figures as specific examples.

[0229] Figures 2 and 4 show the solutions to the Sudoku puzzles shown in Figures 1 and 3, respectively.

[0230] Figure 1 shows that 36 cells are already filled at the start, leaving 45 empty cells for the player to fill. According to the rules of Sudoku, each of the 45 empty cells must be filled using only one number from 1 to 9, such that no cells remain blank at the end, and no numbers can occupy two or more cells in a row, column, or 3x3 block drawn by solid lines that contains an empty cell to be filled.

[0231] The solution to the puzzle is shown in Figure 2, which displays labels corresponding to the algorithm disclosed herein. In this simple problem, only labels A, B, and C needed to be used in the displayed solution. For example, the cell in the first row and sixth column, i.e., cell number (1,6), is filled with the number 9, which is associated with label A. This is because any of the other numbers 1 through 8 would contradict at least one other filled cell or rule. Here, cell number (1,6) could also be tentatively filled with another number. However, placing 9 in another empty cell in the box would contradict the rule that numbers cannot be repeated in a row or column. This is because the number 9 cannot be placed in any other empty cell in the block, since all other empty cells in the 3x3 block have 9 in their corresponding row or column.

[0232] The number 4 in cell (4,8) has label A for a slightly different reason. Any number other than 4 would contradict the cells that were filled at the start. Thus, 1 in (4,8) contradicts 1 in (7,8) because it is a repeat in the same column, 2 contradicts (6,6) because it is a repeat in the same box and contradicts (4,6) because it is a repeat in the same row, 3 contradicts (4,2) because it is a repeat in the same row, 5 contradicts (4,3) because it is a repeat in the same row, 6 contradicts (6,8) because it is a repeat in the same box and the same column and contradicts (4,1) because it is a repeat in the same row, 7 contradicts (6,9) because it is a repeat in the same box, 8 contradicts (5,8) because it is a repeat in the same box, and 9 contradicts (4,9) because it is a repeat in the same box and the same row.

[0233] The number 8 in (4,5) has label B because the numbers 1 through 7 and 9 contradict cells (5,6), (2,5), and (4,7) with respect to 1; (4,6) and (3,5) with respect to 2; (4,2) with respect to 3; (4,8) with respect to 4; (4,3) with respect to 5; (5,4) and (4,1) with respect to 6; (8,5) and (4,4) with respect to 7; and (6,4) and (4,9) with respect to 9. Some of these cells are associated with label A. All other contradictions are with pre-filled cells or cells with labels A or lower. In particular, the number 4, for example, contradicts only cell number (4,8) labeled A, and is therefore excluded. Similarly, the other numbers are excluded because one or more cells are labeled A, and for this reason the 8 in (4,5) is labeled B.

[0234] Cell (6,6) is filled with the number 3 and labeled C. Regarding 4, cell (5,5) and regarding 5, cell (7,6) (both with label B) contradict (6,6), and no cell below label A can exclude the numbers 4 and 5 from consideration.

[0235] When a particular label can be associated with filling a cell, it is worth noting that, generally, higher-ranking labels can also be associated with the same cell, although this is not optimal. In this scheme, to demonstrate inconsistency, it is desirable to select the inconsistent cell for which the label that can be linked to a given cell is the "lowest" label. "Lower" here refers to the preceding label in the alphabetical list of labels used.

[0236] Furthermore, in this method, if the objective is to find the most efficient solution, the numbers can be associated with labels in ascending order for the purpose of calculating a weighted average, and the efficiency of the order is defined such that the lower the weighted average, the more efficient the solution.

[0237] Furthermore, in such a system, it is possible to introduce other selection criteria for conflicting cells. For example, if conflicting cells have the same label, a provision may be made that a cell in the same box as the cell to be filled is selected rather than a cell in the same row or column.

[0238] Other examples of calculating efficiency measures The puzzle in Figure 1 has 45 empty cells. The labels of the solution in Figure 2 are 16 A's, 18 B's, and 11 C's. To quantify the solution, if we assign A's value to 1, B's to 2, and C's to 3, the weighted average of this solution order is (16 + 36 + 33) / 45 = 1.888..., which can be used as a "measure of efficiency" for this solution. Since this is a small number, the corresponding solution (the order in which the cells are filled) can be considered "efficient".

[0239] Optimizing the efficiency measure requires further thought. In this solution, label A is used for one of the contradictory cells, but an inattentive player might use label B if they fail to recognize the options for selecting the order or the rule-based reasoning that would convince them of a lower label. As a result, the efficiency measure (weighted average) of an inattentive player will be higher. For example, while filling in cell (6,6) in the puzzle in Figure 1, a player might overlook the contradiction between the 5 in cell (6,6) and the 5 in cell (7,6), and label B, and instead place label D in cell (6,5) if they determine that it contradicts the 5 in cell (6,5) which has label C, thus potentially increasing the weighted average.

[0240] Errors caused by such careless players can be seen as arriving at the placement of the number 5 in the cell through a different series of steps, and naturally, the weighted average and the level of efficiency of the solution will also differ.

[0241] This method can be used for the puzzle in Figure 3, which has a much longer series of steps. The initial number of empty cells is 49. The distribution of the labels of the solutions given in Figure 4 is 6 A's, 6 B's, 4 C's, 1 D's, 1 E's, 2 F's, 7 G's, 7 H's, 9 I's, and 5 J's, which indicates that determining the correct numbers for multiple cells is much slower, reflected in an approximate weighted average of 5.8163.

[0242] Compared to the puzzle in Figure 1, this puzzle is more difficult, with 49 spaces to fill instead of 45. However, the efficiency measure allows for a much more accurate comparison of the difficulty levels of the two puzzles, with a score of approximately 5.8 compared to 1.8 for the puzzle in Figure 1. This difference is clearly a result not only of the four additional empty spaces in this puzzle, but also of the distribution and number of pre-filled cells, which are reflected as 10 labels A-J, in contrast to the three labels A-C.

[0243] Calculation of efficiency for other puzzle types For other puzzles, alternative instructions may be employed to maintain the order of the steps, formulas to assign values ​​to the steps or labels, and algorithms to calculate a measurable quantity of efficiency. However, the goal of these alternatives is still to calculate a measure of the efficiency of the solution based at least partially on the number and order of steps in the path to the solution.

[0244] Figure 7 shows a partial solution to a puzzle called "Numbrix." The cells are filled with numbers from 1 to 81 in numerical order, not in horizontal or vertical paths. Figure 7 shows some of the cells with labels A, B, C, etc., depending on the stage in which the numbers were determined.

[0245] The cell in the 6th row, 2nd column is filled with 81, but has label M for the following reasons: 80-D at position (7,2) means that 81 could be in (7,3) or (6,2). However, since 56 is in (8,3) and 63 is in (1,3), trying 81 in (7,3) leads to a contradiction. The two available paths between (8,3) and (1,3) end in a contradiction at L, starting from 57-E at (8,4). Therefore, 81 goes into cell (6,2) with label M.

[0246] In the case of this simple puzzle, there aren't many alternative paths, so it can be used for simple competitions.

[0247] Furthermore, the scoring methods described above and for other simple puzzles can be useful in quantified psychological tests to assess or measure progress or regression in a player's cognitive abilities. In fact, the methods of this disclosure for such simple puzzles provide an equivalent to the "maze mouse" experiment, which has been mainstream in conventional psychological experiments.

[0248] In the case of crossword puzzles, another popular puzzle type where you need to fill in cells with letters to satisfy a given clue, you can, for example, adopt a different alphabet letter (e.g., the Greek letters α, β, γ, ...) as a label, and identify two paths to the answer: (1) Start with the letter in the cell, (2) Fill in the cells in the box containing this cell according to the clue to form a word or phrase, (3) Continue filling in cells according to the clue to form a word or phrase in the box where at least one cell is filled and the other cells are not, (4) Identify each filled cell by the letter α, (5) A new "empty" box with no cells filled with letters... It is considered useful to employ a set of instructions and formulas that include: (6) filling in the cells in the crossword puzzle; (7) starting the next sequence in this cell and continuing to fill in cells according to the clues to form a word or phrase in a box where at least one cell is filled and the others are not; (8) identifying each filled cell by the letter β; (9) recursively continuing to fill in the cells of the crossword puzzle in the same way until all boxes and cells are filled; (10) counting the number of cells that have identifiers α, β, γ, ...; (11) assigning a numerical value to each of the letters α, β, γ, ...; and (12) calculating the numerical scale of the answer using a formula based on the values ​​assigned to the letters α, β, γ, ....

[0249] Figure 8 shows a partial solution to a crossword puzzle where some cells are identified by labels α and β. This solution starts with R in the first cell of clue box horizontal 34, then fills in E and B to complete the box, all three of which are identified by α. Next, since the letter R is already filled in, the cell in clue box 3 is dealt with and identified by label α. In the solution, the puzzle solver has reached a dead end with a chain of α, so they must restart from clue box 21, which has no letters horizontally or vertically. It is presumed that by placing the letters F, R, and O vertically and E and D horizontally, each corresponding cell will have the identifier β.

[0250] This diagram shows a partial solution where the process had to be started five times up to that point, in boxes numbered 34, 21, 31, 54, and 25. For readability, other identifiers are not shown, but at least the label identifiers α, β, γ, δ, and ε are used.

[0251] In this case, among several reasonable options for calculating a numerical measure of the efficiency of the step sequence, the simplest is a weighted sum. That is, for each identifier, the product of the number of cells containing that identifier and the value assigned to the label identifier is added. Also, as in the case of Sudoku, a normalized value of the efficiency measure can be calculated.

[0252] Visual depictions of various solutions to the puzzle By using different colors for different labels, this difference can be visually represented, instantly conveying the difference in complexity between the two puzzles.

[0253] Just as the order of completion relates to scoring, it will be recognized that there are many alternatives to defining the order of steps in a crossword puzzle. And finally, one of several mathematical alternatives may be used in the scoring formula.

[0254] By using different colors or other different representations for different labels, this difference can be visually represented, instantly conveying the difference in complexity between the two puzzles. Furthermore, the use of efficiency measures allows for comparison of solutions and inherent difficulty levels of two different puzzles, not just the solutions to the same puzzle, but within a general range.

[0255] Figure 9 visually illustrates the partial structure of the solution in Figure 2, where letters A, B, and C correspond to different graphic patterns. For readability, this depiction simply shows a wavy pattern graphic filling the cell labeled C, but similarly, the other cells can be filled with colors, patterns, or animated graphics to form a collage that reveals the structure of the puzzle.

[0256] Hints for solving the puzzle It is important to note that the structure of a puzzle can only be partially captured by the number of empty cells. The structure of a Sudoku puzzle depends heavily on the distribution of numbers initially placed in the cells, and a graphic representation of such a puzzle can provide far more information about its structure.

[0257] Non-visual cues may be provided based on the methods disclosed herein. As described above, cues may be sound, animation, or video. Cues may also involve other types of input (e.g., olfactory input) or combinations of different types of input.

[0258] The hints must be configurable in a specific order and be related to the discrete steps of the activity. Such a configuration allows for hints that don't reveal too much of the solution, thus preserving the enjoyment of solving the puzzle. At the same time, it helps players who are stuck at a particular point in the activity.

[0259] Furthermore, similar to the coloring of visual hints, sound hints or other types of hints can be predetermined and dynamically communicated to the player when they click on a specific cell at any point or starting point in the puzzle-solving process.

[0260] As mentioned above, in the case of a typical Sudoku, this method may proceed as follows: (1) by linking the stage in which each cell is filled with letters A, B, C, etc., the order in which the cells are filled with numbers 1-9 is recorded to represent the stages and order in which the empty cells are filled; (2) numerical values ​​are assigned to each of the letters A, C, etc.; (3) from the number of cells that have labels A, B, C, etc., and the numerical values ​​assigned to them, a weighted average of the solutions when the cells are filled in the exact order is searched as a measure of the specific path to the solution; (4) two or more solutions (paths) are compared according to their respective measures; and (5) the solutions are ranked according to their respective measures.

[0261] Labels A, B, C, etc. used to obtain rankings may further provide segmentation of the puzzle board or activities. And by using the segmentation, the answers or steps of the activities can be creatively expressed and combined with new artworks, music, and expressions in other media.

[0262] Since the association of labels with the steps of an activity is closely linked to the underlying logical reasons, administrators of games or competitions, etc. may require a specific player or participant to convey the logical reasons for label selection in addition to the logical reasons when filling puzzle cells with letters, for example. As a method of formulating an activity of solving a puzzle, for example, partially, (i) the player identifies the space to be filled and fills it with a given set of letters, (ii) the computer records the step numbers where the spaces are filled, (iii) the player identifies the filling labels, (iv) the player provides the logical reasons for the selection of letters and labels, (v) the computer records the player's reasons together with other data for filling the spaces, (vi) optionally, the computer repeats the recording of data for filling the spaces as necessary, (vii) for verification purposes, the computer uses a record including the cell position, step number, letters, labels, and logical reasons, or the player uses it if changes to the letter arrangement, label, or reason are permitted.

[0263] The activity management organization may permit players to review and modify the placement of characters or labels, etc. in specific situations with specific rules. In a competition, for example, it may permit changes within a very short time after the execution of a step, or, if time remains, permit all players to change their answers at the end. Alternatively, such changes may similarly be permitted for specific classes of players or in other scenarios based on details such as the competition, activity, participants, and environment. Of course, there may also be a one-shot situation / competition where no adjustment of any answer step is permitted after the data has been input.

[0264] Suitable images may be devised and may be used to plead or concisely convey the logical reasons regarding the operations of the user / computer. Such conveyance may be between a player and a computer (or another input / output device), between players / computers, between a player and other entities, or between multiple players. It may also involve (two-way) conveyance to the live or online audience of the activity. In this specification, an example of logical rules and icons edited for Sudoku is given below. These rules and icons are not exhaustive, and additional rules and icons are expected to be added or improved for specific games and activities (including Sudoku).

[0265] Regarding the icons indicating the logical reasons for filling the cells of the puzzle in FIG. 29, they are shown in FIG. 31 according to a set of icons appended to paragraph

[0278] of this specification.

[0266] In implementing the present invention, the provision of specific formats and templates is envisioned to concisely capture data as each step of an activity is performed. For example, data for uniquely identifying and filling each empty space may include a specific filling character, identification of the position in the sequence in which the empty space is filled in the path, a label associated with the filling, and one or more logical reasons for the filling and the corresponding label. Such formats and templates may be particularly useful for communication, for example, when a puzzle-solving competition is held in front of a live or remote audience.

[0267] For example, in a popular Sudoku competition, presenting the data and logical reasoning for filling in each cell can have significant educational value in terms of audience involvement in the solution process and, more generally, in the skill of logical reasoning.

[0268] Selection of solution paths for intended use The disclosure of the parent application envisions the compilation of numerous solution paths submitted by multiple users / players / participants for each puzzle or activity, and after removing any solutions containing errors, a computer system combines them as composite labels associated with the filled spaces in the process of filling in the empty spaces of the puzzle. The reasoning behind such combinations is that the synthesis of multiple past solutions does not discard valid solutions provided to generate hints for subsequent users / players / solvers of the puzzle, and is more useful to human users / players / solvers than hints based on a single solution.

[0269] However, the combination of labels is not suitable for several other conceivable real-world scenarios. For example, the combination of solution paths is not meaningful, especially when solution paths are compared for ranking or rewarding individual trials of an activity.

[0270] In other situations, for example, when team or group members take turns generating a new answer based on hints from past answers and then passing it on to the next member, it is considered desirable to generate hints based on a single answer.

[0271] Even when labels are determined based on a single solution or solution path, it is necessary to determine labels based on correct labeling and to have a plan or procedure for handling solution paths that contain logical errors. In the embodiments presented herein, as an example, paths that do not contain logical errors are separated from paths that do contain logical errors. Paths that do not contain logical errors are placed in the First Subset by the system and recorded in the First database. On the other hand, paths that contain at least one logical error are placed in the Second Subset and recorded in the Second database. This separation allows for flexible management when solutions contain minimal or minor / easily correctable errors.

[0272] Puzzle solution, puzzle complexity, and association of labels with solution steps. There is a complex relationship between the order in which the puzzle-solving steps are executed, the association of labels with those steps, and the complexity of the puzzle. The order in which the empty spaces in the puzzle are filled is dominant over the label associations. However, since there can be multiple directions for the solution path at each step, it is generally impossible to determine the actual order in which the solution steps were executed by looking at the set of labels associated with the steps.

[0273] More complex puzzles generally have longer sequences of related labels than "simpler" puzzles, and in fact, the length of these sequences of related labels is determined, among other factors unrelated to complexity, by the player's skill and attention. Therefore, for example, a skilled player can solve a puzzle using an optimal or shorter sequence of steps and labels than a less skilled player.

[0274] It is precisely this complex relationship between skill and labels that makes it possible to compare puzzle solutions (or paths to solutions) presented by different players. Winning solutions are likely to have a higher frequency of the first letter of the alphabet as labels, and a lower frequency of later letters than lower-ranked solutions.

[0275] Rules for associating labels The following is a precise rephrasing of the basic rule regarding label associations for tracking the execution steps of an activity: Rule: If cell filling is at least partially based on one or more cells associated with a letter preceding the alphabetical letter (selected as the label), but not on any cells associated with a letter not preceding the (selected) letter, then the alphabetical letter is associated with the filling as the label.

[0276] This rule describes a puzzle where empty cells (for example, on a puzzle board) are filled with letters from a given set, but it can be similarly generalized to other activities that can be modeled by such puzzles.

[0277] This labeling rule description avoids circular reasoning while tracking the steps, but provides no other provisions. Therefore, the labels for spaces are not necessarily unique (i.e., not generally unique). A filled empty space in the puzzle may be associated with two or more different labels depending on the filling step in the solution path. Combined with the complexity of the puzzle, this invention advantageously employs this possible multiplicity of labels (often involving multiple steps) to logically distinguish solution paths.

[0278] Logical rules and icons for associating puzzle labels Below are the rules for filling in spaces / cells in puzzles like Sudoku or KenKen, illustrated with different icons that are useful for conveying the logical reasoning behind the steps of filling in empty cells. (1) Based on the given fill cells, only one Character can be filled into the space. (2) Based on a given cell in a row, a specific character can be placed in a single cell in a row. (3) Based on a given cell in place, a specific character can be placed in a single cell in column. (4) Based on the given cells, a specific character can be placed in a single cell in box. (5) Based on cells previously filled (by the player), only one character can be filled into the space. (6) Based on previously filled cells, a specific character can be placed in a single cell in a row. (7) Based on previously filled cells, a specific character can be placed in a single cell in a column. (8) Based on previously filled cells, a specific character can be placed in a single cell in box. (9) If one or more characters can fill a space, then, based on the List of trials, place the same character pair in a cell Pair other than the space in the Row, Column, or Box that contains the space to be filled. (0) If one or more characters can fill a space, then, based on the List of Trials, place the same character Triad in three cells other than the space in the Row, Column, or Box that contains the space to be filled.

[0279] Reason (9) is applicable when the only numbers that can be placed in exactly two cells in the same row, column, or box are the same pair of numbers, and neither of the two numbers can consistently fill a third cell in the row, column, or box.

[0280] Similarly, for reason (0), it applies when there is a triple of numbers in the list of possible numbers for three cells in the same row, column, or box as the cell to be filled.

[0281] Reason (9) helps to remove a pair of numbers for the cell to be filled even before actually trying to fill either of the pair of cells. Reason (0) helps to exclude three numbers from consideration for cells other than the three cells that contain the triple of numbers.

[0282] Both logical rules (9) and (0) reinforce the characteristics of the puzzle that become an exercise in "solving" the cycle of numbers (or letters) filled in the cells by the elimination method by solving puzzles such as Sudoku.

[0283] This group of rules is an example and is not exhaustive. In the case of an 81-cell Sudoku, these logical rules are considered sufficient for labeling. For other puzzles, other or additional rules may be required. Additional rules may also be required to reinforce the process separately. In addition to these rules, it may also be necessary to convey the pre-filled cells used for the designation of characters (numbers) and / or labels.

[0284] Depiction of various solutions to the puzzle by suitable means Although not explicitly shown in this specification, it is easily understood that, for example, by using different colors for different labels, this difference can be visually represented to instantly convey the difference in complexity between two puzzles. The same consideration applies when using auditory differences. By using labels, the difference can also be presented by other suitable means for transmission and / or understanding within or between the solution paths of one or more puzzles.

[0285] Furthermore, it will be recognized that many alternatives exist for defining the order of steps, and that the order of completion is related to the calculation of scoring and efficiency criteria. Many of the mathematical alternatives may be used in the scoring formulas. Also, many alternatives exist for the mathematical calculation of the descriptor values ​​of the solution or solution path, and may be used in the same manner as outlined above.

[0286] By using different colors or other different representations for different labels, differences can be visually represented, instantly conveying, for example, the difference in complexity between two puzzles. Furthermore, the use of efficiency measures allows for comparison of solutions and inherent difficulty levels of two different puzzles, not just the solutions to the same puzzle, but within a general range.

[0287] Hints for solving the puzzle It is important to note that the structure of a puzzle can only be partially captured by the number of empty cells. Regarding characteristics such as complexity, the structure of a Sudoku puzzle largely depends on the distribution of numbers initially assigned to the cells, and a graphic representation of the puzzle based on labels can provide far more information about its structure.

[0288] Furthermore, non-visual hints may be provided based on the methods disclosed herein. As described above, hints may be sound, animation, or video. Hints may also involve other types of input (e.g., olfactory input) or combinations of different types of input.

[0289] The hints must be configurable in a specific order and be related to the discrete steps of the activity. Such a configuration allows for hints that don't reveal too much of the solution, thus preserving the enjoyment of solving the puzzle. At the same time, it helps players who are stuck at a particular point in the activity.

[0290] Furthermore, similar to the coloring of visual hints, sound hints or other types of hints can be predetermined and dynamically communicated to the player when they click on a specific cell at any point or starting point in the puzzle-solving process.

[0291] In particular, with dynamic hints, players may be given some degree of control over factors such as how the hints are displayed, the time elapsed before the hints are provided, the placement of the hints on the puzzle board (to maintain a desired level of cognitive load), and / or the history of hints used by the player. For example, if hints are provided to team members in a competition, such customization would be quite desirable to keep all members engaged.

[0292] As mentioned above, in the case of a typical Sudoku, this method may proceed as follows: (1) by linking the stage in which each cell is filled with letters A, B, C, etc., the order in which the cells are filled with numbers 1-9 is recorded to represent the order in which empty cells are filled and / or the "stages" of cell filling; (2) numerical values ​​are assigned to each of the letters A, B, C, etc.; (3) by using the number of cells tagged with labels A, B, C, etc. and the numerical values ​​assigned to them, a weighted average of the solutions when performed in the strict order of filling the cells is sought in order to obtain a measure of the specific path to the solution; (4) two or more solutions (paths) are compared according to their respective measures; and (5) the solutions are ranked according to their respective measures.

[0293] The method described in the claims can also be used to provide creative insights into the structure of individual puzzles themselves. When spaces are filled at different stages of the process, the method described in the claims can identify spaces by layers (defined, for example, by labels) that are grouped by the points at which these spaces can be filled. Alternatively, it may be possible to group specific spaces by order or "path" that are connected by logical connections that allow players to fill spaces that are related in a chain or tree structure, rather than by their position on the puzzle board.

[0294] Creative expression of puzzle solutions Structures produced by methods described in such patent claims have many potential applications. By visually representing the structure, it becomes possible to simply place and compare two separate puzzles side by side, or combine them to create overlays. More creatively, it is also possible to use the visual representation of the structure as the basis for paintings or other works of art.

[0295] By using puzzle labels, unique representations can be generated. Labels add another dimension to the numbers: filling in the cells of a Sudoku-like puzzle grid. This additional dimension can be used to generate an interesting 3D model of the solution. For example, labels may be distinguished by color, or the numbers placed in the grid of the 3D model of the solution may be distinguished by column height. Alternatively, the numbers in the grid may be distinguished by color, or the column height may correlate with the labels (higher columns representing "higher" labels).

[0296] As is obvious to those skilled in the art, other variations of such model generation methods are feasible. For example, a suitable visual representation of a puzzle can also be used as the basis for the creation of a work of art or the depiction of a performance.

[0297] Another creative use of puzzle structures lies in their role as a foundation for music. While music is created through artistic expression, it shares many similarities with puzzle structures. For example, the key of a written piece, its time signature, or the various chords within a song. Therefore, puzzle structures can also be used as the foundation for yet another musical structure, thereby enabling the generation or composition of music unique to individual puzzles. The pieces of a typical Sudoku puzzle are determined, for example, by a creative interpretation of the dimensions corresponding to the numbers, the labels, and the relative arrangement of the cells filled with both.

[0298] Many or all of the conceivable uses of these described technologies can be incorporated into television programs featuring all of the above-mentioned aspects. Competitors will attempt to complete puzzles, and the efficiency of each solution will be judged. During, between, or at the end of these competitions, composers and dancers may also attempt to create unique songs and dances based on individual puzzles. Judges may also evaluate participants based on criteria such as adherence to the puzzle structure, aesthetic value, and the relative efficiency of their solutions.

[0299] About betting activities based on puzzle solutions As described above, the methods of the present invention can provide opportunities for reward-based skill-based gambling games and activities for entertainment and educational value. Such activities can be conducted in front of an audience, online, via streaming, or through any preferred form of distribution medium. These can be valuable in engaging with logical reasoning, numbers, and mathematical relationships.

[0300] For example, as mentioned earlier, Sudoku games can be used as skill-based betting activities on the internet. Labels allow for measurements such as which row, column, or 3x3 box is filled first and second, which numbers are filled first in all rows, columns, or boxes, or which cells are filled in what order.

[0301] In this scenario, experienced players may be encouraged to solve puzzles and compete for prizes, with each solution serving, for example, to help evaluate the difficulty level. Contributions from various intermediate-level players can also create a realistic level distribution. Beginner or novice players (or the general public) may or may not wish to provide solutions, but may instead place bets on which rows / columns / boxes or other identifiable segments of the puzzle are filled first, second, next, etc. Rewards may also be awarded based on a random draw.

[0302] Furthermore, for the various categories mentioned above, the winning segments and / or cells associated with the best solutions in the case of competitive puzzles can offer revenue generation opportunities, for example, through sponsorships / advertising.

[0303] Similar opportunities can also be used for creative endeavors, for example, by children.

[0304] Regarding the order of filling and the association of labels The detailed logic of the solution attempt requires the transmission of cells that form the basis of the filling. Many alternative methods are possible for this, depending on the player's skill level, age, etc.

[0305] For example, after Player (P) fills the cell used to fill the current cell and taps Rule (R), Computer (C) confirms and records the filling. Alternatively, P fills the cell and taps, C provides options for Rule selection, and P selects a Rule.

[0306] Given the order / filled cells, it is possible to retrospectively associate one (or more) pairs of labels. If logic is available, even if P does not intend an order, the order and reason can work together to associate labels. It is also possible to explore the logic given the order and labels.

[0307] However, even with labels and logic given, it is not possible to search for the order.

[0308] Regarding the use of lowercase letters Using lowercase letters for possible numbers allows us to track the accuracy of our reasoning. This is a good provisional method; it serves as an indicator but not a determinant.

[0309] Examples of activities and games that can be conceived based on this method Puzzle game: Given order and logical reasoning, assign labels.

[0310] Puzzle game: Given labels and order, explore the logic.

[0311] Puzzle game: Improve your "efficiency" score by repeatedly associating labels and refining their order.

[0312] Puzzle game: Gain insight into the links (dependencies) between puzzle cells (nodes) by displaying / mapping the order of filling.

[0313] Cooperative games or puzzle-solving games The puzzle-solving activity can be structured so that the player can have a Logic Buddy.

[0314] It is also possible to structure the solution activity among the team's players. For example, Players I-VI can play as follows: Player I identifies the next cell to fill in. Player II taps the cells to be used in the row, column, and block of the cells to be filled in. Player III identifies the logical reasoning. Player IV enters the graph segments to indicate the order. Player V assigns labels. Player VI scores the solution.

[0315] About the template for recording answers As is evident from the diagram, the provisional or final solution to the puzzle may be displayed in multiple ways. Various templates can be used to display the diverse contents of the filled cells.

[0316] Figure 32 shows an exemplary template that can display entries that can fill in empty cells (a number for the order of filling, an in-cell calculation to find a label to associate with the filling, and a label).

[0317] This method envisions providing the player with templates to select for displaying the final answer and incomplete intermediate answers. It also envisions providing the user with the ability to switch templates during the answer-finding process.

[0318] In rows, columns, or boxes, if only two or three cells remain to be filled, using a scratch template makes it easier to see and allows you to display all cells to be filled or all cells filled up to the step of filling the current cell.

[0319] For two or three cells in a row, column, or box of Sudoku, if the only possible entry is a cycle of two or three numbers, the calculation leading to the label association follows the reasoning shown in Figures 22 and 23.

[0320] Additional points to note regarding the implementation of the method The embodiments described above can be implemented in any of many ways. For example, some aspects of the embodiments may be implemented using hardware, software, or a combination thereof. In the case of a software implementation, the software code can be executed on a suitable processor or group of processors, whether provided on a single computer or distributed across multiple computers. Naturally, one or more controllers that control the functions described above can be any or a group of components that perform the functions described above. One or more controllers can be implemented in many ways, such as dedicated hardware or general-purpose hardware (e.g., one or more processors) programmed with microcode or software that performs the functions described above.

[0321] In this regard, naturally, one embodiment of the present invention comprises at least one non-transient computer-readable storage medium (e.g., computer memory, floppy disk, compact disk, tape, etc.) on which a computer program (i.e., a set of instructions) is encoded, which, when executed on a processor, performs the functions of the embodiments of the present invention. The computer-readable storage medium may be transportable so that the embodiments of the present invention described herein can be realized by loading the stored program onto any computer resource. Also, naturally, the reference to a computer program that, when executed, performs the functions described above is not limited to an application program running on a host computer. Rather, in this specification, the term "computer program" is used in a general sense to represent any type of computer code (e.g., software or microcode) that can be employed to program a processor to realize the embodiments of the present invention described above.

[0322] Since various embodiments of the present invention can be used individually, in combination, or in a variety of configurations not specifically discussed in the embodiments described above, the details and configurations of the components described or drawn above are not limited to those described in each application. For example, an embodiment described in one embodiment can be arbitrarily combined with an embodiment described in another embodiment.

[0323] Furthermore, embodiments of the present invention can be implemented as one or more methods for which an example has already been provided. The operations performed as part of this method can be ordered in any preferred manner. Thus, embodiments can be configured in which the operations are performed in a different order than those exemplified, and even if some operations are shown as sequential operations in the exemplary embodiments, several operations can be performed simultaneously.

[0324] In the claims, the use of ordinal terms such as “first,” “second,” and “third” to modify claim elements does not, in itself, imply any priority, preference, or order of one claim element to another, nor any temporal order in which the actions of the method are performed. Such terms are used merely to describe a particular named claim element and to distinguish it from other elements of the same name or descriptor (except for the use of ordinal terms).

[0325] The expressions and technical terms used herein are for illustrative purposes only and should not be considered limiting. The use of “including,” “comprising,” “having,” “containing,” “involving,” and their variations includes the following and additional items.

[0326] Finally, while many explanations use representations suitable for puzzles like Sudoku, where cells or spaces are actually filled in, many methods, techniques, and procedures are applicable to other games and activities if they can be modeled by logical puzzles.

[0327] Furthermore, this specification describes the capabilities and requirements of computer machines and networks that enable the execution of various processes. These machines can be configured as subsystems within a large engine or platform that enables the multiple applications outlined above. These machines not only hold large amounts of data but also perform tasks such as verifying the association of solution steps and labels, and generating integrated labels and hints.

[0328] Although several embodiments of the present invention have been described in detail above, it is expected that those skilled in the art will readily conceive of various modifications and improvements. These modifications and improvements are included within the spirit and scope of the present invention. Therefore, the above description is merely an example and is not intended to limit the invention in any way.

Claims

1. A method for associating the execution order and labels of steps for solving a puzzle with respect to one or more parts of one or more solution paths of a puzzle, using a computer system, The computer system includes at least one computer device or a network of computer devices. The puzzle has a given configuration consisting of a set of spaces, a given set of different letters, and a given set of rules. The aforementioned set of spaces, if filled with characters, includes one or more non-empty spaces. The step of solving the puzzle comprises selecting from a given set of different characters and filling one of the one or more empty spaces with a character that is consistent with the given set of rules and, if the set of spaces contains one or more non-empty spaces, with the given one or more non-empty spaces in the set of spaces, The puzzle is solved by one or more steps of filling in one or more empty spaces in the set of spaces, The puzzle is solved when, by the step of solving the puzzle, all of the one or more empty spaces in the set of spaces are filled. The path to the solution, i.e., the solution path, is a series of two or more steps that solve the puzzle, which is linked in the same order so that two or more corresponding empty spaces among the one or more empty spaces are filled. A first step of the solution path has no preceding step, and in the first step of the solution path, one of the one or more empty spaces is filled with one of the given set of different characters based on the given set of rules and the given one or more non-empty spaces in the set of spaces. A second or subsequent step of the solution path comprises filling one of the one or more empty spaces with one of the given set of different characters, based on the given rule, the given one or more non-empty spaces in the set of spaces, and the character that was filled in one of the one or more empty spaces during one or more preceding steps of the solution path. The method for associating the labels with one or more parts of a solution path is: (a) An operation that provides a set of labels {Label(1), Label(2), ..., Label(I), ...} whose order is known, (b) An operation to receive a labeling algorithm that associates labels with filling empty spaces in the solution path, wherein Label(1) is associated with the first step of the solution path, and each empty space filled in a second or subsequent step of the solution path is associated with a label based on the known label order in the set of labels, (c) An operation to receive the first step of the first solution path into the computer system, (d) The operation of receiving the association of Label(1) with the empty space filled in the first step of the first solution path into the computer system, (e) The operation of recording the association of Label(1) with the empty space filled in the first step of the first solution path, (f) If a next step exists in the first solution path, the operation of receiving the next step into the computer system, (g) An operation to receive the association of the label with the empty space filled in the next step by the labeling algorithm, (h) recording the label associated with the empty space filled in the next step in the computer system, (i) If the following solution path exists, the operation of receiving the first step of the following solution path into the computer system, (j) The operation of receiving the association of Label(1) with the empty space filled in the first step of the next solution path into the computer system, (k) If the next solution path has a next step, the operation of receiving the next step into the computer system, (l) The operation of receiving the association of the label with the empty space filled in the next step in the next solution path by the labeling algorithm, (m) The operation of recording the label associated with the empty space filled in the next step in the next solution path in the computer system, (n) The computer system performs an operation to determine whether a label associated with filling a given empty space for any of the one or more solution paths is inconsistent with a given set of rules, a given non-empty space in the set of spaces, or an empty space filled in any preceding step of the solution path. (o) The computer system performs an operation to identify from one or more solution paths a first subset of the solution paths in which there are no labels associated with filling empty spaces that do not correspond to one of the given set of rules, a given non-empty space in the set of spaces, or an empty space filled in a preceding step of the solution path, (p) The computer system performs an operation to identify from one or more solution paths at least one label associated with filling empty spaces that does not correspond to one of the given set of rules, a given non-empty space in the set of spaces, or a second subset of the set of solution paths that was filled in a preceding step of the solution path, (q) The operation of recording in a first database each solution path in the first subset and the label associated with filling the empty space, (r) The operation of recording each solution path in the second subset in the second database along with the label associated with filling the empty space, A method that includes [a certain feature].

2. The given set of distinct characters is {Char(1), Char(2), ..., Char(I), ..., Char(λ)}, and is identified collectively as {CHARS}. The aforementioned set of spaces is {Space(1), Space(2), ..., Space(I), ..., Space(σ)}, and is identified collectively as {SPACES}. The set of rules, which includes a given set of rules and logical constraints for associating the filling of empty spaces in the puzzle with labels, is {Rule(1), Rule(2), ..., Rule(I), ... Rule(ρ)} and is collectively identified as {RULES}, For integers J and K (1 ≤ J ≤ λ and 1 ≤ K ≤ σ), filling Space(K) with the letter Char(J) is associated with the aforementioned series of labels, If the aforementioned filling is consistent with any given non-empty space in {RULES} or {SPACES}, then Label(1) is associated with the filling of Space(K) by the character Char(J), The method according to claim 1, wherein if the filling is consistent with a Rule in the set {RULES} or a given non-empty space in {SPACES}, Label(1) is associated with a filling of Space(K) with the character Char(J), or labels Label(1), Label(2), ..., Label(I-1) are associated with a filling of spaces other than Space(K) with the character {CHARS}.

3. (s) A step of examining the labels associated with the steps that solve the puzzle, starting with the first label which is determined to be inconsistent with one of the given set of rules, a given non-empty space in the set of spaces, or an empty space filled in any preceding step of the solution path in the second database, (t) The step of replacing the first mismatch label to eliminate the mismatch, (u) A step of exchanging the labels of the subsequent steps for solving the puzzle as a result of exchanging the inconsistent labels, (v) The computer system determines whether a new label associated with the filling of a given empty space in the solution path as a result of the exchange is inconsistent with one of the given set of rules, a given non-empty space in the set of spaces, or an empty space filled in any preceding step of the solution path. (w) If, after the exchange, the label associated with the subsequent filling of spaces in the solution path does not match one of the given set of rules, a given non-empty space in the set of spaces, or an empty space filled in any preceding step of the solution path, the step of repeating steps (s), (t), (u), and (v) (x) The step of moving the solution path from the second database to the first database, The method according to claim 1, further comprising:

4. The operation that receives the association of the label with the empty space filled in the previous step by the labeling algorithm is: (g1) The computer system performs an operation to search for the location in the sequence where the empty space was filled by the provider of the solution path, (g2) The computer system provides the provider with the order in which the empty spaces in the solution path are filled, (g3) The computer system records the order in which the empty spaces in the solution path are filled, The method according to claim 1, comprising:

5. The computer system performs the operation of holding the record, (g31) An action by the computer system to prompt the provider of the solution path to fill the empty spaces with specific characters, based on the rules, constraints, and data assigned or logically derived from a given set of information, and to communicate one or more logical reasons relating the filling of the empty spaces to the labels, (g32) The computer system performs an operation to receive one or more of the logical reasons, (g33) The computer system records data for the unique identification and filling of the empty space, including the specific character that was filled, the identification of the position of the empty space in the path in the order in which it was filled, the label associated with the filling, and the one or more logical reasons. The method according to claim 4, comprising:

6. The operation by which the computer determines whether a label associated with a given empty space is inconsistent with one of the given set of rules, a given non-empty space in the set of spaces, or an empty space filled in any preceding step of the solution path, (n1) As an attempt to solve the puzzle, the operation of provisionally filling the empty spaces with one of each of the given set of different characters, (n2) For each trial attempt to solve the puzzle that resulted in a trial error where the solution to the puzzle was not completed, the number of steps from filling the empty space with the characters to a logical error is counted, (n3) For each trial error, the operation of saving the minimum number of steps until the logical error, (n4) An operation to confirm that the empty space is filled with only one of the given set of distinct characters that does not end in a logical error, (n5) An action to confirm that the label associated with the step of filling the empty space follows the series of labels at a distance greater than the minimum number of steps for all of the trial errors, The method according to claim 1, comprising:

7. When calculating numerical values ​​for a set of labels associated with filling a given empty space in the solution path, (s) A step of providing a series of ordered numbers, (t) A step of assigning one of the series of numbers to each of the series of labels while maintaining the correspondence in order between the series of numbers and the series of labels, (u) The step of receiving an expression for calculating the sum of the numerical values ​​assigned to multiple labels in the set of labels, (v) The step of calculating the sum of the set of labels using the formula above, The method according to claim 1, comprising:

8. When numerically ranking two or more sets of labels associated with filling a given empty space in one or more solution paths, (w) The step of receiving the numerical value assigned to each of the two or more sets of labels associated with filling the empty space in each of the one or more solution paths, (x) The step of calculating the sum of each of the two or more sets of labels using the above formula, (y) A step of ranking the two or more sets of labels in an order derived from comparing the sum of the multiple sets of labels, The method according to claim 7, further comprising:

9. When ranking is performed by comparing two or more parts of one or more solution paths in the first database, (w) an operation to receive a label associated with the space in each of the two or more parts of the solution path, (x) an operation to receive the numerical value assigned to the label associated with the space in each of the two or more parts of the solution path, (y) An operation to calculate the sum of the labels of each of the two or more parts using the above formula, (z) An operation to rank the two or more parts of the one or more solution paths in the order derived from comparing the sums of each of the two or more parts, The method according to claim 7, further comprising:

10. When numerical ranking is performed across two or more segments of a given set of spaces by comparing one or more of the solution paths in the first database, (w) an operation to receive labels associated with each of two or more segments of a given set of spaces for one or more of the solution paths in the first database, (x) an operation to receive the numerical value assigned to the label associated with the space in each of the two or more segments of the given set of spaces, (y) An operation to calculate the sum of each of the two or more segments using the above formula, (z) An operation to rank the two or more parts of the one or more solution paths in the order derived from comparing the sums of the two or more segments, The method according to claim 7, further comprising:

11. Based on past solutions available in the first database, in order to generate dynamic hints for the player, (s) The step of receiving the location of the current space or the empty space to be filled from the player, (t) The step of receiving from the player one or more parameters that define the range of space in the given set where the next hint is to be placed, (u) Based on past answers, the player is given the following hints: the location of a space to be filled within the range defined by the player, or the location of at least one empty space that, if filled, would give a solution path to the space within the range; The method according to claim 1, further comprising:

12. Based on one or more solutions available in the first database, in order to generate dynamic hints for a new player, (s) A step of receiving the new player's preference for the pace at which to receive hints, (t) A step of receiving a preference for a positional range in the puzzle from the new player to receive hints for filling all the spaces, (u) The step of receiving the location of the empty space to be filled from the new player, (v) For a new player, the step of generating a hint for solving the puzzle or a hint for taking a new solution path by using a label synthesized and integrated by the preferences set by the new player, The method according to claim 1, further comprising:

13. The method according to claim 1, wherein the solution path is a path that completes the solution to the puzzle.

14. (z) The method of claim 8, further comprising the step of selecting one or more sets of labels as the winning set based on the ranking order.

15. (aa) The method of claim 9, further comprising the step of selecting one or more sets of labels as winning portions of the one or more solution paths based on the ranking order.

16. (aa) The method of claim 10, further comprising the step of selecting one or more sets of labels as a winning segment based on the ranking order.

17. The method according to claim 7, wherein the purpose of calculating the sum of the set of labels is to reward one or more sets of winning labels, one or more winning portions of the one or more solution paths, or one or more winning segments of the one or more solution paths.

18. The method according to claim 17, wherein the victory is a selection based on participation in a predetermined number of user groups.

19. The method according to claim 17, wherein the win is a selection based on bets placed by one or more predetermined user groups.

20. The method according to claim 1, wherein one or more of the steps received by the computer system are collaboratively prompted by two or more human players.

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