Calcudoku Puzzle

A Latin square with arithmetic bolted on

Fill every cell so each row and each column holds 1 to N exactly once. That part is Sudoku without the boxes. What makes it Calcudoku is the cages: bold-outlined groups of cells, each labelled with a target and an operation that the numbers inside have to produce.

So the two rule systems constrain each other. The cage tells you what a small group of numbers multiply to; the row tells you which of those numbers are still available. Neither is enough alone, and the puzzle is the traffic between them.

Every sheet is built from a fresh seed, so thirty pupils can have thirty different grids.

Reading a cage

The label sits in the top-left cell of its cage. The number is the target and the symbol is the operation.

7+ means the numbers inside add to 7. 12× means they multiply to 12. 2− means the difference between the two is 2, larger minus smaller, and 3÷ means the larger divided by the smaller gives 3.

Two things worth knowing before you start. Subtraction and division only ever appear on two-cell cages, because a difference between three numbers is not well defined. And a single-cell cage is simply the value that goes in that square, written as an addition target, which makes it the free gift on the board.

Where to start

Single-cell cages first. They cost nothing and each one immediately removes a number from a row and a column.

Then the most restrictive two-cell cages. A large product or a large difference usually has only one or two possible pairs on a small grid, and on a 4×4 a cage marked 12× has to be 3 and 4. Pencil in the candidates for each cage, then let the Latin-square rule do the elimination: once a row holds certain numbers, the remaining cells can only take what is missing, and that frequently resolves a neighbouring cage outright.

Work back and forth between the arithmetic and the row logic. A clean Calcudoku never needs a guess.

4×4 or 5×5

The 4×4 uses 1 to 4 and is a genuine five-minute puzzle. It is the right introduction, and it is small enough that a child can hold the whole board in their head.

The 5×5 uses 1 to 5, fits more cages, and produces noticeably longer chains of reasoning. The arithmetic does not get harder, which is the point: the largest number in play is still a five, so the puzzle tests deduction rather than calculation at both sizes.

Why it works in a maths lesson

A cage marked 12× rehearses factor pairs. One marked 7+ rehearses number bonds. A child working through a grid does dozens of both without once being asked to recall a fact, because the recall is instrumental rather than the task.

That is a different experience from a page of sums, and it lands with children who have decided they are bad at maths, because the thing they are visibly good at is the reasoning.

Print several, hand out the puzzle pages and keep the answer pages, and press Generate New whenever you want a completely different arrangement of cages.