Odd-Even Sudoku is a variation of the classic Sudoku puzzle that adds an extra rule related to the parity (odd or even) of the numbers in the grid. The rules for an Odd-Even Sudoku on a 9×9 grid are as follows:
1. The grid is divided into nine 3×3 sub-grids, also known as “boxes” or “regions.”
2. Each row of the grid must contain the numbers 1 to 9, with no repetition of numbers within the row.
3. Each column of the grid must also contain the numbers 1 to 9, with no repetition of numbers within the column.
4. Each 3×3 sub-grid must contain the numbers 1 to 9, with no repetition of numbers within the sub-grid.
5. In addition to the above rules, there is an extra constraint related to the parity of the numbers. The numbers in the even cells (cells with a square symbol) must be even numbers (2, 4, 6, or 8), and the numbers in the odd cells (cells with a circle symbol) must be odd numbers (1, 3, 5, or 7).
6. The puzzle starts with some numbers already filled in, known as “clues” or “givens.” These numbers are the starting point for solving the puzzle.
7. The goal of the puzzle is to fill in the remaining empty cells with numbers from 1 to 9, following the rules above, so that each row, column, and 3×3 sub-grid contains all the numbers 1 to 9 without any repetition, and the additional odd-even constraint is also satisfied.
8. As with the classic Sudoku, there is only one solution to a valid Odd-Even Sudoku, and it can be achieved through logical deduction without any guessing or trial-and-error.
