How to Solve Calcudoku: Beginner Strategies Step by Step

To solve Calcudoku you do two jobs at once. The cages tell you which digits can go in a few cells, and the rows and columns tell you where each digit cannot go. The method below keeps both jobs in order. If the rules are not clear yet, start with the Calcudoku rules.

A five-step method

1. Write the free digits. A cage with one cell and no sign gives its digit. Write it, then cross it off in its row and column.
2. List the digits of each small cage. For a cage of two or three cells, write the few digits that fit its product or sum in the corner of each cell.
3. Use full lines. In a 5 x 5 grid each row adds up to 15, in a 4 x 4 grid to 10, in a 6 x 6 grid to 21 and in a 7 x 7 grid to 28. When a cage covers all but one or two cells of a line, the rest is arithmetic.
4. Place by exclusion. If a digit can be in one cell only of a row or column, it goes there.
5. Return to the cages. Each digit you place removes possibilities from other cages. Go back to step 2 for those cages.

Every LogikLand grid is kept only if a solver can find the solution by deduction, so this loop always finishes without a guess.

Products and sums to know

In a 5 x 5 grid the digits are 1 to 5. These cages have a single possible set of digits when their cells are in a row or column (so the digits are all different):

Sums over two cells are just as short: in a 5 x 5 grid 3+ is 1 and 2, 4+ is 1 and 3, 8+ is 3 and 5 and 9+ is 4 and 5, because two equal digits are not allowed side by side. For subtraction and division, the possibilities depend on the grid size, but they stay short: in a 5 x 5 grid, 4− is only 1 and 5, and 3÷ is only 1 and 3.

Straight cages and L-shaped cages

A cage in one row or one column has all its digits different, so a product has few possibilities. A cage in an L shape or another bent shape has two cells that are not in the same row or column, and those two may hold the same digit. This is why bent cages often hide a pair of equal digits. In the example below, the L-shaped 16× can be 4, 1, 4, which a straight cage never could.

Walkthrough on a 5 x 5 grid

This is a medium LogikLand grid. We write (row, column) from the top left, 1 to 5.

First moves

1. The cell (5,2) is a cage with a single cell and no sign: it is 5. Cross 5 off in row 5 and in column 2.
2. The first column has a cage 30× with three cells in rows 3 to 5. The only three digits from 1 to 5 with product 30 are 2, 3 and 5. So rows 3, 4 and 5 of column 1 hold 2, 3 and 5, and rows 1 and 2 hold the two other digits, 1 and 4.
3. At the top left, the L-shaped cage 16× covers (1,1), (2,1) and (2,2). Its cells (1,1) and (2,1) are 1 and 4 from step 2. If (1,1) were 1 and (2,1) were 4, the third cell would be 16 ÷ (1 × 4) = 4, a second 4 in row 2. That is impossible, so (1,1) = 4, (2,1) = 1, and (2,2) = 16 ÷ (4 × 1) = 4. The two 4s of the cage are allowed because they are in different rows and columns.
4. The cage 8× in the last column has two cells, (2,5) and (3,5), so they are 2 and 4. Row 2 already has a 4 at (2,2), so (2,5) = 2 and (3,5) = 4.
5. Cross 4 off in row 3 and in column 5. In row 5, the 5 from step 1 means (5,1) cannot be 5, so (5,1) is 2 or 3.

From here, the same loop gives the rest of the grid one cell at a time. Check yourself against the solution on the right.

Mistakes beginners make

• Using a digit twice in a straight cage. In a row or column cage, all digits differ.
• Ruling out a repeated digit in a bent cage. A bent cage may hold the same digit at its two ends.
• Reading − and ÷ in the wrong order. You always take the larger digit first: 2− means larger minus smaller equals 2.
• Repeating a digit in a row because its two cells belong to different cages. The cages never change the row and column rule.
• Skipping the sum of the row. It is a strong check once a few cells are known.

How to practise

Start with 4 x 4 grids. You can print six from printable easy Calcudoku puzzles. Move to 5 x 5, where subtraction appears, then to 6 x 6, which adds division. When you want harder logic, read advanced Calcudoku techniques. To make your own grids or a whole book, create a free account and use the Calcudoku assistant.