Arithmetic Game Strategy Using Segmented Integer Fields
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Solution Overview
Problem
Existing arithmetic games lack a structured method for players to strategically combine and manipulate single-digit integers using arithmetic functions to achieve a target value, limiting the variety and complexity of solutions.
Innovation Solution
The game involves selecting a set of single-digit integers and applying arithmetic functions like addition, subtraction, multiplication, and division to generate subsequent fields, allowing players to strategically combine and operate integers to reach a target value, with the option to flip digits and carry integers between fields.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If players are given freedom to choose any arithmetic operations and combinations, then the variety of solutions and player engagement increase, but the game structure becomes too complex and difficult to manage
Solution Approach 1:
The patent segments the arithmetic problem-solving process into distinct phases: an initial field of single-digit integers, intermediate subsequent fields generated by arithmetic operations, and a final target field. This segmentation structures the complexity by breaking down the overall problem into manageable stages, allowing players to systematically work toward the target value while maintaining game structure.
Solution Approach 2:
The patent changes parameters such as the number of integers in each field, the types of arithmetic operations available, and the target value to create varying levels of difficulty and strategic depth. By adjusting these parameters, the game can adapt to different player skill levels while maintaining a structured framework that prevents overwhelming complexity.
2Adaptability or versatility
If the game allows multiple subsequent fields and strategic selections, then the depth of strategy and replayability increase, but the time required to complete a game increases
Solution Approach 1:
The patent requires players to pre-select a specific quantity of initial integers before generating the initial field. This preliminary action sets clear boundaries and expectations for the game, allowing players to mentally prepare for the strategic decisions ahead while preventing indefinite extension of the game. The predetermined field size creates a natural time constraint that balances strategic depth with game completion time.
3Ease of operation
If the game uses only single-digit integers, then the mathematical operations remain accessible to all players, but the range of possible combinations and solutions is limited
Solution Approach 1:
The patent implements a nested structure where single-digit integers from the initial field are combined to form multi-digit integers in subsequent fields. These subsequent fields then become new sources of single-digit integers for further operations. This nesting allows the game to maintain accessibility through single-digit operations while generating unlimited combination variety through the creation and decomposition of multi-digit numbers across multiple fields.
Data Source
AI summary
An arithmetic game is played by selecting a target value that is an integer between 1 and 9. A field of initial integers is selected and subsequent fields of integers are generated by strategically selecting and combining integers from the field of initial integers or from another subsequent field of integers. At least one combined integer or at least one operated integer is added to, subtracted from, multiplied by, or divided by at least one other combined integer or at least one other operated integer to produce at least one sum, difference, product, or quotient that is a calculated integer. Subsequent fields of integers are created until a target field is created with no carried integers and the remaining calculated or combined integers are added, subtracted, multiplied, or divided to produce a sum, difference, product, or quotient that is the target value.