AZTest
← All logic puzzles

Calcudoku

A Latin square where every cage does its sum.

Start level 1 48 levels

Loading the levels…

How to play

  • Fill each row and column with the numbers 1 to N, each once.
  • The numbers in a cage combine with its operation to make its target.
  • For − and ÷ the cage has two cells, taken larger first. A one-cell cage gives its number.

The Latin Square Property

Every row and every column must contain each number from 1 to N exactly once. No number may repeat in any row or column.

3+6×1−4+1123312231
✓ Correct Every row and column contains digits 1 to 3 exactly once, with no duplicates.
3+6×1−4+1223312231
✗ Wrong Row duplicate: the top row contains two 2s. A number cannot appear more than once in the same row.
3+6×1−4+1113312231
✗ Wrong Column duplicate: the middle column contains two 1s. A number cannot appear more than once in the same column.

Subtraction (−)

A subtraction cage always has two cells. Subtract the smaller number from the larger to match the target clue. Numbers can appear in either order.

2−1−21−2−312123231
✓ Correct Larger minus smaller: 3 − 1 = 2 (target 2−) and 2 − 1 = 1 (target 1−). The larger number may be in either cell.
2−1−21−2−213321132
✗ Wrong Wrong difference: 2 − 1 = 1, but the cage target is 2−.
2−1−21−2−312231123
✗ Wrong Wrong difference: 3 − 1 = 2, but the cage target is 1−.

Division (÷)

A division cage always has two cells. Divide the larger number by the smaller to reach the target integer. The quotient must be exact with no remainder.

2÷3÷2÷3÷3÷3÷2÷2÷4213243113423124
✓ Correct Larger divided by smaller: 4 ÷ 2 = 2 (target 2÷) and 3 ÷ 1 = 3 (target 3÷). Works in either cell order.
2÷3÷2÷3÷3÷3÷2÷2÷3214243113424123
✗ Wrong Remainder not allowed: 3 ÷ 2 = 1.5, which is not an integer. Division must divide evenly without remainder.
2÷3÷2÷3÷3÷3÷2÷2÷4123243113423214
✗ Wrong Wrong quotient: 4 ÷ 1 = 4, but the cage target is 2÷.

Addition (+)

All numbers inside the cage must add up to the target clue.

3+6+5+4+123231312
✓ Correct Sum equals target: 1 + 2 = 3 (target 3+), 2 + 3 = 5 (target 5+), and 3 + 1 + 2 = 6 (target 6+).
3+6+5+4+321213132
✗ Wrong Wrong sum: 3 + 2 = 5, but the cage target is 3+.
4+6+5+4+223312131
✗ Wrong Duplicate in row: even though 2 + 2 = 4, repeating 2 in the same row violates the Latin square rule.

Multiplication (×)

All numbers inside the cage must multiply together to produce the target clue.

6×2×3×2×3231312123
✓ Correct Product equals target: 2 × 3 = 6 (target 6×) and 3 × 1 = 3 (target 3×).
6×2×3×2×3123231312
✗ Wrong Wrong product: 1 × 2 = 2, but the cage target is 6×.
6×2×3×2×3312231213
✗ Wrong Wrong product: 2 × 2 = 4, but the cage target is 3×.
A small Calcudoku, solved.