How to play Calcudoku

Calcudoku is a math grid puzzle. Each row and column holds each number once, like Sudoku. Outlined groups of cells must reach a target with a math sign.

Other names for Calcudoku

Calcudoku and Mathdoku are two names for the same puzzle. KenKen is the trademark of a similar puzzle with the same basic rules. Cross Sums has no connection to KenKen.

The rules

1. A grid of 4 × 4 cells uses the numbers 1 to 4. A grid of 6 × 6 uses 1 to 6, and so on.
2. Put each number once in each row and once in each column.
3. Thick lines split the grid into cages. Each cage shows a target and a sign: + (add), − (subtract), × (multiply) or ÷ (divide).
4. The numbers in a cage must reach the target with that sign. For − and ÷, take the larger number first: 3 − 1 = 2, and 4 ÷ 2 = 2.
5. A cage of one cell has no sign. Write its target in the cell.
6. A number can repeat inside a cage, if the cage covers more than one row and column and the row and column rules still hold.

A worked 4 × 4 example

Try this puzzle first, then read the steps. It uses the numbers 1 to 4.

Step 1: fill the one-cell cage

The cage "4" has one cell, so that cell is 4.

Step 2: list the two-cell cages

• 6+: two different numbers from 1 to 4 that add up to 6 are 2 and 4.
• 3÷: 3 ÷ 1 is the only way, so the cells are 1 and 3.
• 4÷: 4 ÷ 1, so the cells are 1 and 4.
• 7+: 3 + 4, so the cells are 3 and 4.

Step 3: solve the bottom row

The bottom row has the 4÷ cage, so its right two cells are 1 and 4. The 6+ cell in the bottom row cannot be 4 too, so it is 2, and the cell above it is 4. The bottom row now needs a 3, so the 3÷ cell in the bottom row is 3. The cell above it is 1.

Step 4: finish the grid

• The second column has 4, 1 and 3, so its empty cell is 2.
• The 6× cage now needs two numbers that multiply to 3 (6 ÷ 2). They are 1 and 3.
• The third row has 4 and 1, so its right cells are 2 and 3. The 7+ cage allows only 3 or 4 there, so it is 3. The right cell is 2, and the 7+ cell above is 4.
• The 2÷ cage is 2 with 1 or 4. The second row already has a 4, so the cell is 1.
• The second row then needs a 3 on the left, so the top left cell is 1.
• The third column has 4 and 3, and the 4÷ cell in it must be 1 or 4. So it is 1, and the bottom right cell is 4.
• The top row needs 2 and 3. The third column needs a 2, so the top row is 1, 4, 2, 3. Check the 1− cage: 3 − 2 = 1.

First solving methods

• Fill the one-cell cages first. They are free numbers.
• List the options for small cages. Two cells with 3÷ in a 4 × 4 grid can only be 1 and 3.
• Break × targets into factors. 12× in two cells of a 4 × 4 grid is 3 × 4. 24× in three cells is 2 × 3 × 4.
• Use the row total. Each row of a 4 × 4 grid adds up to 1 + 2 + 3 + 4 = 10. In a 6 × 6 grid, each row adds up to 21. If a row has one cell outside its cages, subtract to find it.
• Remove numbers the row or column already has. This is often the step that fixes a cage.

Kakuro uses the same kind of sum logic. See how to play Kakuro and the Kakuro combinations chart.

Play Calcudoku on iPhone

Cross Sums has a free daily Calcudoku and a free daily Kakuro, with no ads. See the app.