Open-Source Paper on a Sudoku (Sumdoku)-Inspired Puzzle Game with Number Placement and Arithmetic

Abstract
This paper introduces a new Sudoku-like puzzle game using a 7x7 grid with numbers ranging from 1 to 49, with no repetition of numbers. The game requires players to strategically place numbers to achieve specific total sums for rows and columns. The goal is to engage enthusiasts who enjoy puzzles involving number placement and arithmetic. This paper and the game are provided for free as an open-source project, accessible to all programmers interested in developing and expanding the game.

Introduction
Sudoku is a popular number-placement puzzle that has inspired numerous variants. This paper presents a unique twist on the traditional Sudoku rules by expanding the grid to 7x7 and using a wider range of numbers. In addition to filling the grid, players must ensure that the sums of numbers along each row and column meet specific criteria. This open-source project aims to contribute to the puzzle and gaming community by offering a new challenge that combines Sudoku principles with arithmetic requirements.

Game Overview

Grid Description: The puzzle consists of a 7x7 grid, where each cell must be filled with numbers from 1 to 49, without repeating any number.

Total Sums Calculation:

• An additional row and column, considered the “8th grid,” are used to display the sums of the corresponding rows and columns from the main 7x7 grid.
• Each sum in the vertical row must equal the corresponding sum in the horizontal row, resulting in 2x totals of the same value for each 7-cell set.

Rules and Requirements

Number Placement: The numbers 1 through 49 must be placed in the grid without repetition.
Sum Constraints:

• The sums of the numbers for each row (1–7) must equal the sums for each corresponding column (1–7).
• The sums are calculated and displayed in the 8th row and column of the grid. Challenge Factor: The game is designed to challenge the player to not only fit the numbers correctly but also meet the arithmetic requirements for each row and column sum.

Implementation and Development Guidelines
This paper provides a link to an Excel spreadsheet where a playable version of the game is available for download. The spreadsheet can be used to understand the game mechanics, test solutions, and serve as a foundation for programming a digital version.

Programmers and developers are encouraged to build upon this concept by:

Creating digital implementations of the game in various programming languages.
Extending the rules or creating new game modes.
Sharing their implementations as open-source projects.

Technical Considerations

Algorithm Suggestions: For those programming the game, techniques for ensuring unique number placement and sum calculations will be discussed.
Testing and Debugging Tips: Guidance on verifying the correctness of row and column sums during gameplay.
Sample Code: Examples in Python or JavaScript to help programmers get started.

Lessons Learned and Future Directions
The process of designing this game highlighted the balance between number placement and arithmetic strategy. Possible future developments include expanding the grid size, adding constraints or bonuses, or creating competitive modes.

Conclusion
This Sudoku-inspired game aims to provide an entertaining and educational challenge for players and developers alike. As an open-source project, the goal is to foster creativity and collaboration within the programming community. By freely offering this paper and the Excel spreadsheet, I hope to encourage programmers to innovate and share their own versions of the game.

Download and Contribution
A link to download the Excel spreadsheet version of the game will be provided below. Contributions and suggestions are welcome, and developers are encouraged to share their implementations and modifications.

Acknowledgments
This paper and the associated resources are provided as an open-source gift to the programming community, with the hope of inspiring further exploration and development of puzzle-based games.

Thank you
Sipho Masilela (16/10/2024)
siphosumdoku@gmail.com
link to excel: https://docs.google.com/spreadsheets/d/1M7JFXWfqd7PZPysdlW9FSaEpd0DEeQpm/edit?usp=sharing&ouid=111064438879543272416&rtpof=true&sd=true

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