5x5 Calcudoku Puzzles

With five digits and ten to twelve cages, the 5x5 calcudoku is where the game finds its balance: enough cages with a single answer to start, enough open cages to make you think. Each row and column holds the digits 1 to 5 once, and each cage shows the number its digits must make with the operation written beside it.

The twelve puzzles come in three sets of four: addition only, where a row adds up to 15; addition and subtraction, where the minus cages are pairs; and all four operations, where a 30× cage can only be 2, 3 and 5. Every grid has one solution, reached by logic alone, and the book gathers the twelve pages.

Part of the Calcudoku Puzzles collection, Last updated on Tue, 27 Oct 2026 17:54:55 GMT.

Free Printables

5x5 Calcudoku with Addition, Puzzle 1

5x5 calcudoku with addition only, eleven cages: a single cell of 5, six two-cell cages (4+, 5+, 5+, 6+, 8+ and 9+, the last one being 4 and 5) and four three-cell cages (7+, 8+, 9+ and 9+). Addition, puzzle 1 of 4. | zuzuzi.com

5x5 Calcudoku with Addition, Puzzle 2

5x5 calcudoku with addition only, eleven cages and no given digit: eight two-cell cages, among them two of 3+ (1 and 2 each) and three of 6+, and three three-cell cages (11+, 12+ and 12+, a 12+ in a line being 3, 4 and 5). Addition, puzzle 2 of 4. | zuzuzi.com

5x5 Calcudoku with Addition, Puzzle 3

5x5 calcudoku with addition only, twelve cages: three single cells (3, 5 and 5), five two-cell cages (3+, 5+, 6+, 7+ and 7+) and four three-cell cages (6+, 6+, 11+ and 11+). Addition, puzzle 3 of 4. | zuzuzi.com

5x5 Calcudoku with Addition, Puzzle 4

5x5 calcudoku with addition only, ten cages and no given digit: six pairs (5+, 5+, 5+, 8+, 8+ and 9+), three three-cell cages (4+, which is 1, 1 and 2 around a corner, 5+ and 12+) and a four-cell 14+. Addition, puzzle 4 of 4. | zuzuzi.com

5x5 Calcudoku with Addition and Subtraction, Puzzle 1

5x5 calcudoku with addition and subtraction, ten cages: two single cells (1 and 5), a 3− pair, two addition pairs (3+ and 6+), three three-cell cages (9+, 10+ and 10+) and two four-cell cages (10+ and 14+). Addition and subtraction, puzzle 1 of 4. | zuzuzi.com

5x5 Calcudoku with Addition and Subtraction, Puzzle 2

5x5 calcudoku with addition and subtraction, eleven cages and no given digit: two subtraction pairs (1− and 3−), six addition pairs (3+, 4+, 4+, 4+, 5+ and 6+) and three three-cell cages (7+, 12+ and 14+, which must repeat a 5). Addition and subtraction, puzzle 2 of 4. | zuzuzi.com

5x5 Calcudoku with Addition and Subtraction, Puzzle 3

5x5 calcudoku with addition and subtraction, eleven cages: a single cell of 5, four subtraction pairs (1−, 1−, 2− and 2−), two addition pairs of 4+ and four three-cell cages (6+, 11+, 11+ and 14+). Addition and subtraction, puzzle 3 of 4. | zuzuzi.com

5x5 Calcudoku with Addition and Subtraction, Puzzle 4

5x5 calcudoku with addition and subtraction, ten cages, six of them subtraction pairs (1−, 2−, 2−, 2−, 3− and 3−), with three three-cell cages (9+, 11+ and 12+) and a four-cell 14+. Addition and subtraction, puzzle 4 of 4. | zuzuzi.com

5x5 Calcudoku with All Operations, Puzzle 1

5x5 calcudoku with all four operations, eleven cages: a single cell of 3, two 1− pairs, a 5× pair and a 5÷ pair (1 and 5 each), two addition pairs (6+ and 9+) and four three-cell cages (8×, 9+, 9+ and 10+). All operations, puzzle 1 of 4. | zuzuzi.com

5x5 Calcudoku with All Operations, Puzzle 2

5x5 calcudoku with all four operations, ten cages and no given digit: a 12× pair (3 and 4), four addition pairs (5+, 6+, 7+ and 9+) and five three-cell cages (4×, which is 1, 1 and 4 or 1, 2 and 2, then 6+, 9+, 10+ and 10+). All operations, puzzle 2 of 4. | zuzuzi.com

5x5 Calcudoku with All Operations, Puzzle 3

5x5 calcudoku with all four operations, eleven cages: two single cells (1 and 3), a 1− pair, a 20× pair (4 and 5), two addition pairs (5+ and 6+) and five three-cell cages (6×, 10×, 10+, 12+ and 12+). All operations, puzzle 3 of 4. | zuzuzi.com

5x5 Calcudoku with All Operations, Puzzle 4

5x5 calcudoku with all four operations, eleven cages: a single cell of 5, two 1− pairs, two 6× pairs, a 2÷ pair, a 9+ pair (4 and 5) and four three-cell cages, 12×, 30× (2, 3 and 5), 7+ and 9+. All operations, puzzle 4 of 4. | zuzuzi.com

How to Solve a 5x5 Calcudoku

List the cages with a single answer first: 3+ is 1 and 2, 9+ in two cells is 4 and 5, 4− is 1 and 5, 5÷ is 1 and 5, 20× is 4 and 5, and a three-cell 6+ in a line is 1, 2 and 3. Then use the rule of 15: every row and column adds up to 15, so the cells of a row left outside its cages add up to 15 minus the cage sums, a trick that often fixes a lonely cell. Write candidates small, cross out what each placed digit forbids in its row, column and cage, and remember that a bent cage may repeat a digit while a straight one never does.

Frequently Asked Questions

Which cages have a single answer in a 5x5 grid?

Among pairs: 3+ (1 and 2), 9+ (4 and 5), 4− (1 and 5), 5÷ (1 and 5), 20× (4 and 5), 2× (1 and 2) and 12× (3 and 4). Among three cells in a line: 6+ (1, 2 and 3), 12+ (3, 4 and 5), 30× (2, 3 and 5) and 60× (3, 4 and 5). They are the first digits of almost every grid.

Why do some grids have a cage with a single cell?

Because a cage of one cell is simply a given digit. The generator uses one or two of them in some grids to keep a single solution without adding more cages.