Calcudoku: play calcudoku online free

Calcudoku is a Latin square with arithmetic. Fill an N×N grid so every row and column holds 1 to N, while each outlined cage makes its target using the operation shown. Play calcudoku online free here, on grids from 5×5 to 8×8.

It is the same idea as the KenKen-style puzzles you may know from newspapers: no 3×3 boxes, just rows, columns and a little mental arithmetic.

The rules

• The grid is N×N (5×5 to 8×8 here). Fill it with the digits 1 to N.
• Each row and each column contains every digit from 1 to N exactly once. There are no boxes.
• Heavy outlines mark cages. Each cage shows a target and an operation: + (add), − (subtract), × (multiply) or ÷ (divide).
• Combine the digits in a cage with its operation to make the target. For − and ÷, a cage has two cells: take the smaller from the larger, or divide the larger by the smaller.
• A single-cell cage simply gives its digit.
• A digit may repeat inside a cage, as long as the repeats are not in the same row or column.

How to start

Start with the forced cages

Some cages can only be made one way. In a 5×5 grid, 4− must be 5 and 1, 20× in two cells must be 4 and 5, and 6× in two cells must be 2 and 3. A 2÷ cage is 1 and 2 or 2 and 4; 3÷ is 1 and 3.

Use row and column totals

Every row and column of an N×N calcudoku adds up to N(N + 1)/2 and multiplies to N!. That is 15 and 120 for 5×5, 21 and 720 for 6×6, 28 and 5,040 for 7×7, and 36 and 40,320 for 8×8. If cages cover a row except for one cell, the totals give you that cell, just like the rule of 45 in killer sudoku.

Think in prime factors

On grids up to 8×8, the only digit divisible by 5 is 5 itself, and the only one divisible by 7 is 7. So a × cage whose target is a multiple of 5 must contain a 5, and one that is a multiple of 7 must contain a 7. Large × targets are usually the easiest cages to pin down.

Calcudoku is pure Latin-square reasoning, which our solving techniques guide covers in depth.

Common mistakes

• Worrying about the order in − and ÷ cages. Always take larger minus smaller, or larger divided by smaller.
• Assuming digits can’t repeat in a cage. They can, if the repeats are in different rows and columns, as in an L-shaped cage.
• Looking for 3×3 boxes. Calcudoku only has rows, columns and cages.
• Forgetting that digits only run up to N. A 5×5 grid has no 6.

How the ranks scale difficulty

The same four ranks apply here as everywhere on the site. Lemma is a gentle warm-up, Proposition needs a real idea or two, Theorem is near-minimal with almost every clue load-bearing, and Conjecture is the sparsest of all, so expect to think hard.

Calcudoku grids run from 5×5 to 8×8. Bigger grids mean more combinations per cage, so the arithmetic and the Latin-square logic both get richer.

There are 99,999 puzzles per rank, each with its own number, so you can replay one or share it. Every type also has a 30-puzzle collection that climbs from Lemma to Conjecture. Every puzzle is checked to have exactly one solution that you can reach by logic alone, with no guessing.

Keep exploring

• Killer SudokuCages with sums instead of given digits. Partition arithmetic and the rule of 45.
• FutoshikiA Latin square with < and > signs between neighbouring cells.
• KakuroA numerical crossword: runs of distinct digits 1–9 that hit their sums.
• Solving techniquesSingles, pairs, cage arithmetic, line logic and Latin squares, all in one guide.
• All puzzle guidesEvery puzzle type on Hoot’s Puzzles, with rules and tips.