Mathrax – Hard

To print multiple puzzles at once, click here.

Mathrax is a logic puzzle played on a square grid. The objective is to fill each cell with numbers from 1 to N, where N is the size of the grid's side. Each row and column must contain each number exactly once, similar to Sudoku. Additionally, circles placed at intersections provide extra conditions that must be met.

Basic Rules

• No number may appear more than once in any row or column.
• Some intersections contain circles with additional constraints that affect the four diagonally adjacent cells.

Additional Rules

• A circle may contain a number and a mathematical operation (+, −, ×, ÷). The number inside the circle represents the result of applying the operation to the four diagonally adjacent numbers.
• A circle may contain the letter "E" (even), meaning that all four diagonally adjacent numbers must be even.
• A circle may contain the letter "O" (odd), meaning that all four diagonally adjacent numbers must be odd.

Basic Solving Tips

• Use row and column uniqueness: Since each row and column must contain unique numbers from 1 to N, check for missing numbers.
• Work with given operations: If a circle shows an operation, try finding possible number pairs that satisfy the equation.
• Check parity hints (E/O): If a circle has E, all adjacent numbers must be even, reducing possibilities. Likewise, an O restricts choices to odd numbers.
• Look for unavoidable numbers: Some cells may have only one valid choice based on previous placements and constraints.