Method to create jigsaw like puzzles with completely defined solutions

Abstract

A typical jigsaw has these characteristics: Planar and without voids when complete Has tabs (extensions) and sockets (internal voids) to maintain relative alignment of the pieces Most often a pleasing image on just one side Most often rectangular Many pieces, hundreds to thousands Edge and corner pieces Presently available jigsaw puzzles have difficulty added by: Increasing the number of pieces Making the pieces of multiple shapes Making the puzzle with a complex image Making the puzzle double sided Making the puzzle with transparent pieces What if a puzzle had these characteristics: Planar and without voids when complete Has tabs and sockets to maintain an assembled shape No image either side No preferred face No preferred orientation Few pieces All pieces of a similar shape? This PCT application describes a method to make a set of interconnecting jigsaw-like pieces with the goal of maximum difficulty to assemble using least pieces. The method includes the selection of the shape of puzzle pieces, the shape of a whole minimal- piece-count puzzle and methods to decouple visual features of manufactured pieces to not-aid assembly, thereby providing a greater challenge to the person assembling the puzzle. Puzzles described herein are capable of being assembled from one to many ways to make a snow-flake-like shape, according to their label. This method provides a means of knowing all solutions for any given puzzle. Knowing all solutions enables a given the puzzle to be graded on a scale of 1 to 10. The puzzle community subjectively rate puzzles of many kinds from 1 to 10.

Description

[Method to create jigsaw like puzzles with completely defined solutions]

[0001] Toys and puzzles

[0002] WIPO advice: indicate the background art which, as far as known to the applicant, can be regarded as useful for the understanding, searching and examination of the invention, and, preferably, cite the documents reflecting such art. Jigsaw puzzles are so common that it is assumed the reader is familiar with this concept and art is not required. In the context of this application let the words puzzle and jigsaw be used interchangeably. Let a puzzle be a set of essentially planar interconnecting pieces which when joined make a planar surface without voids.

[0003] The author had thought that by reviewing the features of jigsaws generally that it might be possible to create the most difficult jigsaw with least pieces. To this end a shape for jigsaw pieces and the jigsaw as a whole were investigated. Hexagonal pieces were found to have the most orientations and 7 hexagonal pieces made a compact snowflake-like puzzle. A simple naming schema allowed puzzles to be graded by the number of solutions they offered and the pieces could have their manufactured asymmetries decoupled. This provides a set of 7 pieces with only their tab and socket positions for assembly information

[0004] To create jigsaw-like puzzles of greatestdifficultyusing the least pieces.

[0005] Select a puzzle shape that provides the greatest level of connectivity and greatest number of similar physical presentations when rotated or flipped [Fig.1,2].

[0006] The preferred piece shape is a hexagon providing six presentations per puzzle piece.

[0007] The overall puzzle shape is that of a centre hexagonal piece with 6 surrounding pieces, this provides a snow-flake like seven piece puzzle.

[0008] Create a naming schema so that puzzle pieces can be logically defined.

[0009] Create a naming schema for their interconnections to be defined.

[0010] Create computer software to generate logical solutions to make a numerical representation of a set of puzzle pieces that will interconnect when converted to a physical form [Fig.9,13].

[0011] This software also determines the complete list of 7-piece-solutions and 6-piece-assemblies for a given puzzle set. A 6-piece-assembly awaits its seventh piece, if it will connect.

[0012] Use commercially available software to make a master parametric drawing for one puzzle piece from which all puzzle pieces are derived.

[0013] The puzzle set data can be used to make the puzzle pieces completely free of transcription errors [Fig.12,13].

[0014] Create a manufacturing schema that decouples as many visual and textural differences of the physical pieces as possible.

[0015] To this end numerically based manufacture ( eg 3D printing ) provides a low cost path as no physical tooling is required.

[0016] Most manufacturing processes generate parts with discernable textures or asymmetries.

[0017] The manufacturing schema described herein negates this issue by randomly flipping and rotating the pieces programmatically before manufacturing begins, so the texture and orientation of the faces provide no assembly information.

[0018] This method provides a means of manufacturinguniquepuzzles with all solutions known.

[0019] The puzzle pieces can be made to be unique within a set and have only tab and socket positions to facilitate their interconnection.

[0020] With all solutions known the puzzles can be graded bydifficulty.

[0021] A graphical plot can be made with a vertical scale ( y ) of 1 to 10 units and a horizontal scale ( x ) of total number of solutions for many puzzles.

[0022] y=10-logbase3( x )

[0023] The graph is a straight line, a useful metric in itself and a cross check for computational correctness. The scaling to a level of 10 is synthetic. It is an attempt to grade the puzzles for the puzzle community. In practice any puzzle above level 6 is difficult, and the scale is base 3 exponential in nature.

[0024] A unique serial number can be created from puzzle parameters which identify each puzzle. The preferred method is the use of a public file transfer checking algorithm called a Cyclic Redundancy Check, CRC. Let the word CRC mean the result of any algorithm used for the purpose of detecting any change in a list of data. In a schema using seven hexagons the CRC preferrebly uses p0,p1,p2,p3,p4,p5 of each piece, i.e. 42 integers. Other cryptographic methods such an SHA could also be used. Additions to the pool of puzzle solutions, created but yet to be made, are filtered out using their CRC, if they are duplicates of prior solutions. Another property of a CRC or like data check is that they are not reversible i.e. a set of pieces cannot be decoded by this number.

[0025] The puzzle serial number can be used for quality assurance and as an identifier in any instance of copying as it is unique and recorded.

[0026] Provides absolutely unique puzzles for which there is no method for their assembly. No generic solution can be published.Fig.1

[0027] A common jigsaw piece is shown with its sides made straight so that it can connect with 4 presentations if double sided. A presentation is one of a set of possible orientations that look similar. The design requirement of pieces being similar in shape, to aid in overwhelming a person’s short term memory, means that triangle and squares / rectangles and hexagons are the only shapes providing a planar surface with no voids. A triangular base shape provides limited symmetry and would need many pieces to provide difficulty. Few pieces is another design goal..Fig.2

[0028] The preferred hexagonal shape is shown which allows 6 presentations.Fig.3

[0029] For clarity, a perspective of a hexagonal piece is shown with its legend. The legend is made separately alongside the puzzle piece and denotes its orientation. X-X = 1-3 means that it is piece 1 in orientation 3.Fig.4

[0030] An outline of the preferred shape of a hexagon is shown. Its tabs are labeled p0,p2,p4 and its sockets numbered p1,p3,p5. The set p0,p1,p2,p3,p4,p5 numerically define the piece. Its manufactured dimensions are not critical and a matter of aesthetics.Fig.5

[0031] A parametric drawing is shown. The actual dimensions of the piece are in an accompanying list contained in the file for the drawing package in use.The preferred edge length is 30mm and the tabs and sockets 10mm in diameter. The exact dimensions are fine tuned for tactile properties. An essential feature of the parametric drawing is that a piece set p0,p1,p2,p3,p4,p5 can be used to set the positions of the tabs and sockets in any manufactured piece.Fig.6

[0032] The preferred hexagonal pieces when made into a set of 7 make a showflake like shape. This assembly is the goal for the puzzle.Fig.7

[0033] A computer program written for the purpose creates a set of 7 pieces using random integers and connection rules dictated by the puzzle shape, a snowflake in this discussion,shows a partial listing for the solutions to a chosen set. When many solutions are considered and the total solutions are plotted a log-linear graph can be made. The graph also contains a “cloud” of 6-piece-assemblies. Considering a puzzle of level 4 and projecting into the cloud it can be seen there are approximately 16,000 6-piece-assemblies of which around 1000 can be completed. Further, consider two single solution data points 1BAFA973, has 126 6-piece-assemblies, and D08DF314 10270 6-piece-assemblies. In each case only one of the 6-piece-assemblies will yield a solution. Reaching the point of a 6-piece-assembly for single solution puzzles is difficult. The reader can see that completeing a single solution puzzle will be difficult in the extreme.Fig.8

[0034] A puzzle is deemed to be completed when its set of pieces are joined to a contiguous planar surface, in this example the snowflake-like shape. The orientation of the puzzle is unimportant.Fig.9

[0035] A part photograph of a puzzle is shown with its defining label.

[0036] HEXX.au is the product web page

[0037] 1-1 signifies it is a 1 permutation puzzle with 1 solution.

[0038] X97F82AA is its serial number, in this case a CRC.

[0039] 10.0 is its designated level of difficulty. The puzzle community subjectively rate puzzles on a scale of 1 to 10 in their difficulty to complete.

[0040] Note the different texture of the visible faces of the pieces, this is due to the decoupling of orientation from the numerical description of the piece.Fig.10

[0041] Code snippet testing for correct interconnections of pieces.Fig.11

[0042] Code snippet showing the simplicity of virtual rotation and flipping of a piece prior to manufacture.Fig.12

[0043] Code snippet that is used with the parametric drawing to make an entire set of files for manufacture from one puzzle set definition.Fig.13

[0044] A partial listing of a puzzle solution showing the derived serial number and difficulty level with the first few lines of a solution listing.Fig.14

[0045] An image of several contemporary puzzles adding difficulty to their solution.Fig.15

[0046] Glossary of terms.

[0047] The motivation for the puzzle was to make a jigsaw of greatest difficulty with least pieces.

[0048] Considering the limited short term memory of humans ( seven pieces of information ) puzzle pieces with the least variation and most possible orientations were preferred.

[0049] Given the availability of information ( the internet ) puzzles which are unique were preferred, so that published solutions had no application.Process to create a numeric puzzle solution

[0050] The preferred shape of a puzzle piece is a hexagon with 3 tabs and 3 sockets.

[0051] The puzzle piece shape neatly arranges into a seven piece puzzle.

[0052] The physical size of the puzzle pieces is not important; 30mm on edge is preferred.

[0053] A thickness of 5mm is preferred.

[0054] Each puzzle piece can be described by its set of connection indexes

[0055] Numerical description of one piece +2,+2,-2,0,0,0

[0056] Numerical description of a set of seven pieces is P0,P1,P2,P3,P4,P5,P6

[0057] Each index translates into a physical offset distance clockwise around the piece.

[0058] Looking at a given edge an index of zero is the centre of the edge, and index of +1 is one unit clockwise along the edge. The preferred size of this offset is in the millimeter range.

[0059] The physical size of one unit offset is fixed for all pieces of a given puzzle but may vary from puzzle to puzzle.Steps to generate a puzzle solution.

[0060] An offset extent is chosen, 1 = (-1,0,+1), 2=( -2,-1,0,1,2 ) etc.

[0061] An offset extent of 1 unit will yield mostly easier puzzles.

[0062] An offset extent of 2 units will yield mostly difficult puzzles.

[0063] Each piece is assigned a null state.

[0064] Beginning with P0 each of its six connections are randomly assigned an offset.

[0065] Choosing P1, P1[3] = -P0[0], the remainder are set randomly.

[0066] Choosing P2, P2[4] = -P0[1].

[0067] P2[5] = -P1[2], the remainder are set randomly., and so on.

[0068] The piece interconnections are listed in.

[0069] Once a numerical set for a puzzle has been created proprietary software tests every piece placement and orientation of each piece to see if another solution is possible. [Fig.9,13] shows a tested solution with a few lines of its complete definition.

[0070] Now that a numerical solution is defined it is sorted into a pool of solutions from which to make a physical puzzle.

[0071] Commercially available software is used to define a generic puzzle piece as a parametric drawing.

[0072] Any puzzle solution can be copied from the pool of solutions into a software script written for the purpose to manipulate the parametric drawing to produce a set of files to be sent to a printer. Let the word printer be used herein to refer to any device capable of accepting numerical control for the production of the puzzle pieces. Laser cutting, electric discharge machining, routing etc. are other production possibilities but 3D printing is preferred as the pieces are efficiently presented as a set for assembly.

[0073] In the manipulation of the parametric drawing each puzzle piece is logically altered so that the piece being drawn is randomly rotated or flipped to one its 6 possible orientations.

[0074] By this means any manufacturing asymmetry or imperfections carry zero information for the purposes of assembling the puzzle.

[0075] Seven files, one for each piece are transferred to a printer and the set of pieces printed together with their legends.

[0076] One puzzle piece, chosen randomly, will have had the puzzle identifying information printed upon it. In practice a person attempting to assemble a puzzle will orient this piece so the text is legible, however because the piece has a random orientation and every orientation of a completed puzzle is regarded as the same solution, this is not a clue to a assembly.

[0077] Once printed a puzzle can be quickly assembled using its legend for quality assurance prior to its immediate bagging. The legend is discarded..

[0078] From WIPO SCP / 9 / 5,March 17 / 2003,age 2 part 6

[0079] In relation to the second point, the EPO Boards of Appeal have held that the requirement for industrial applicability implies a “commercial exploitation,” with the purpose of achieving “financial gain” (see Board of Appeals decisions T204 / 93; T144 / 83).

[0080] As this method supports a puzzle for commercial sale it meets the requirement of Industrial Applicability.Patent Literature

[0081] PTL1:

[0082] https: / patentscope.wipo.int / search / en / result.jsf?_vid=P22-M3CBRS-60892

[0083] FP:(hexagonal jigsaw puzzle)

[0084] 1.20060232006Intelligence jigsaw puzzle

[0085] 2.210813873 Hexagonal puzzle frame

[0086] 3.213724789 Six-cylinder double-position three-dimensional jigsaw puzzle intelligence toy

[0087] 4.1476492 THERAPEUTIC JIGSAW

[0088] 5.9075 Jigsaw puzzle of hexagonal cubes

[0089] 6.1244502 FLAT PATTERN CONSISTING OF HEXAGONAL TILES WITH DEFORMED EDGES

[0090] 7.WO / 2000 / 045914FLAT PATTERN CONSISTING OF HEXAGONAL TILES WITH DEFORMED EDGES

[0091] 8.2000039593 Flat pattern consisting of hexagonal tiles with deformed edges

[0092] AU - 26.10.2000

[0093] Int.Class A63F 9 / 20 Appl.No 39593 / 00 Applicant Hinderer, Jurgen Inventor Hinderer, Jurgen

[0094] The invention relates to a set or a plurality of 14 different tiles which differ in type, and notably in colour, between which a dividing line can extend and which can be assembled in the manner of a jigsaw puzzle to form a flat pattern. The shape of the individual tiles is based on regular hexagons whose edges can be deformed in a particular manner. The shape and number of different types of edges is determined on the basis of a mathematical model and based on the presence or absence of a colour transition or a dividing line to adjacent tiles. In this way eight different edges are created from which six pairs can be formed. The tiles provided for in the invention oblige a user to fit said tiles together correctly and at the same time permit the creation of a multitude of different flat tiling patterns. The invention can be used as a jigsaw puzzle or flat surface cover.

[0095] 9.104354980 Anti-burglary children swallowing protecting plastic welding cover with jigsaw function

[0096] 10.5368301Double sized puzzle

[0097] 11.213432980 Novel educational toy for preschool education

[0098] 12.2502506 Board game of domino or jigsaw type - comprises playing board, with hexagonal playing pieces fitting onto it.Non Patent Literature

[0099] Images of a range of contemporary puzzles trying various strategies to make a jigsaw more difficult.

Claims

A hexagonal base-shape is preferred for the puzzle pieces as this shape has the largest number of presentations, six per piece [Fig.2].Puzzle pieces can be described with a simple set of connecting positions (p0,p1,p2,p3,p4,p5), and the puzzle with a simple set of pieces, (P0,P1,P2,P3,P4,P5,P6), independently of any physical considerations [Fig.3,6].The method decouples all visual / textural differences of its pieces, resulting from the chosen method of manufacture, from their placement and orientation in a puzzle [Fig.9,12].The whole method of manufacture allows the creation of the most difficult single solution puzzles, with least pieces. Paragraph 33 and [Fig.7].Every puzzle can be proven to be unique via its CRC.The use of random numbers for generating tab and socket positions with attendant interconnection rules means that there is no method or technique available to solve a puzzle, by a person or a machine, other than by trial and error.The similar shape of the puzzle pieces and simple interconnecting rules allow all solutions to be known, thus a given puzzle can be numerically graded in difficulty. This is important as the effort required to assemble a puzzle increases by a factor of 3 for each increase in its difficulty index by one unit [Fig.7].The method described herein allows the packaging of puzzles with zero errors as the physical embodiment of the puzzle, which is manufactured-as-a-set, is immediately assembled-as-a-set once made, or wholly rejected.The method is free of transcription errors.

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