Even-Odd Sudoku – Hard

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Even-Odd Sudoku is a variant of the classic Sudoku puzzle. In this version, certain cells are marked with gray circles or squares to indicate whether they should contain even or odd numbers, providing additional clues to solve the grid.

Basic Rules

1. Grid Structure: The puzzle consists of a 9x9 grid, divided into 3x3 subgrids (also known as regions or boxes).
2. Number Placement: Each row, column, and 3x3 subgrid must contain all of the numbers from 1 to 9, without repetition.
3. Even/Odd Indicators: Cells with gray circles must contain odd numbers (1, 3, 5, 7, 9), while cells with gray squares must contain even numbers (2, 4, 6, 8).

Additional Rules

• Unique Solution: The puzzle must be solvable to one unique solution.
• Initial Numbers: The grid is pre-filled with some numbers to allow a unique solution.

Basic Solving Tips

• Single Possibility: If a cell has only one possible number that can be placed in it, fill it in.
• Single Candidate: For each box, row, and column, if a number can only be placed in one cell, fill it in.
• Exclusion: Exclude numbers from cells based on the numbers already placed in the same row, column, or box.
• Even/Odd Consideration: Utilize the even/odd indicators to narrow down the possibilities for a cell.

Tips Specific to Even-Odd Sudoku

• Even/Odd Exclusion: Use the even/odd indicators to immediately exclude certain numbers from consideration in a cell.
• Cross-Checking: Use the even/odd indicators in conjunction with other filled cells to cross-check and validate possible numbers.
• Pencil Marks: Use pencil marks to keep track of possible numbers in a cell, and update them as you gather more information from the grid.