Bingo Face Generation Using Relatively Prime Column Sets

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Solution Overview

Problem

The existing methods for generating unique number combinations in games like Bingo face significant challenges due to the vast number of possible combinations, leading to prohibitive storage requirements and lengthy duplicate checks, making it inefficient to create and store large quantities of non-repeating bingo faces.

Innovation Solution

The method employs the concept of relatively prime numbers to generate unique bingo faces by selecting and combining sets of numbers in a pairwise fashion, using a processor-based algorithm that selects columns of numbers from finite sets, ensuring all combinations are unique without the need for extensive storage.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Ease of manufacture

If completely random number generation is used to create unique bingo faces, then the simplicity of the generation process is maintained, but the storage requirements and duplicate checking time become prohibitively large

Engineering Contradiction:

Improvesimplicity of generation processVSAvoidstorage requirements

Core Design Contradiction:

Ease of manufactureVSQuantity of substance

Solution Approach 1:

The patent divides the 75 numbers into five separate sets (1-15, 16-30, 31-45, 46-60, 61-75), with each set assigned to a specific column. This segmentation allows the system to generate unique bingo faces by combining column selections rather than storing all possible combinations, dramatically reducing storage requirements while maintaining uniqueness through the mathematical properties of relatively prime numbers.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent changes the approach from storing complete bingo face combinations to storing only column selection parameters. By using relatively prime numbers to determine column selections and generating faces through combination of these parameters, the system reduces storage from sextillions of bytes to manageable quantities while ensuring uniqueness through mathematical properties.

Inventive Principle:

Principle #35Parameter changes

2Reliability

If all possible unique bingo face combinations are stored in memory, then complete uniqueness is guaranteed, but the storage space and processing time become prohibitively large

Engineering Contradiction:

Improveuniqueness guaranteeVSAvoidstorage space

Core Design Contradiction:

ReliabilityVSVolume of stationary object

Solution Approach 1:

The patent pre-establishes five sets of columns with relatively prime numbers before bingo face generation. These pre-configured column sets serve as the foundation for generating unique faces through combination rather than storage, ensuring uniqueness is built into the generation process itself rather than verified afterward through exhaustive storage and comparison.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The patent introduces column selections as an intermediary mechanism between the desired output (unique bingo faces) and the underlying number combinations. By selecting columns based on relatively prime numbers and combining them, the system generates unique faces without needing to store or compare all possible combinations, using the column selection process as a mediator that guarantees uniqueness.

Inventive Principle:

Principle #24Intermediary (Mediator)

3Adaptability or versatility

If more bingo faces are stored in memory to ensure uniqueness, then the variety of unique faces increases, but the time required for duplicate checks increases proportionally

Engineering Contradiction:

Improvevariety of unique facesVSAvoidduplicate checking time

Core Design Contradiction:

Adaptability or versatilityVSLoss of time

Solution Approach 1:

The patent replaces the mechanical process of storing and comparing complete bingo face combinations with a mathematical system based on relatively prime numbers. Instead of physically storing and searching through vast numbers of combinations, the system uses number theory properties to guarantee uniqueness, substituting computational mathematics for brute-force storage and comparison methods.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

4Adaptability or versatility

If a 5x5 bingo face with standard number ranges is used, then the traditional bingo format is maintained, but the number of unique combinations reaches over 111 quintillion requiring immense storage

Engineering Contradiction:

Improvetraditional bingo formatVSAvoidnumber of combinations

Core Design Contradiction:

Adaptability or versatilityVSQuantity of substance

Solution Approach 1:

The patent adds a dimensional layer to bingo face generation by introducing column-based selection with relatively prime numbers. Instead of treating each bingo face as a single 111-quintillionth combination, the system organizes numbers into five dimensional columns with specific number ranges, where uniqueness is achieved through the mathematical relationship between column selections rather than exhaustive combination storage.

Inventive Principle:

Principle #17Another dimension (Dimensionality change)

Data Source

PatentUS8577943B2Algorithm for creating unique bingo faces

Publication Date: 2013.11.05 ARROW INTERNATIONAL INC

AI summary

A method and apparatus for generating a plurality of unique configurations of indicia is provided. A first set of indicia is provided, including a plurality of first groups of indicia. Then a second set of indicia is provided that has a plurality of second groups of indicia. The first set of indicia is then combined with the second set of indicia in a pairwise fashion, wherein a number of the first groups of indicia is relatively prime in relation to an number of the second groups of indicia.