Cross Math: rules and how to play

Goal of the game

Fill the number cells so that every horizontal and vertical equation reaches its printed result. The same cell participates in two equations.

Rules

• On an N×N number grid, use each integer from 1 to N² exactly once across the whole grid: 1–4 for 2×2, 1–9 for 3×3. Keep given numbers.
• Operators and results are fixed. Read rows left to right and columns top to bottom.
• Use standard precedence: multiplication and division before addition and subtraction; operations at the same priority go left to right. There are no parentheses.
• Each division must give an integer at the point it is evaluated. Results can be greater than the largest number you may enter.

A small example, step by step

1. In a 3×3 example, a row reads 2 + _ × 3 = 14.
2. Do the multiplication before the addition. Subtract 2 from the target: the product must be 12.
3. The missing number is 4, since 4 × 3 = 12 and 2 + 12 = 14.
4. Check that 4 is unused elsewhere and satisfies its column. The row alone does not finish the grid.

Beginner deductions

• Start with equations containing only one empty number cell, working backwards from the result.
• Maintain the set of unused numbers for the entire grid. Every filled cell removes one number from that set.
• With two unknowns, list ordered pairs that satisfy the equation, then use their columns or rows to exclude pairs. Order matters for subtraction and division.

Common mistakes

• Do not calculate everything left to right: 2 + 4 × 3 is 14, not 18.
• Do not reuse a number merely because it is in another row.
• Do not swap the operands of a division to make it work, or accept an intermediate fraction.