Puzzle rules

A Mathdoku is an arithmetic grid puzzle: a Sudoku-like Latin square crossed with mental arithmetic. Two kinds of constraint shape every puzzle — rows and columns, and cages.

What is Mathdoku?

A Mathdoku puzzle is an n×n grid — anywhere from 2×2 to 9×9 — that you fill with the numbers 1 through n. Unlike Sudoku there are no given digits sprinkled around the grid. Instead, the grid is carved into outlined regions called cages, and each cage carries a small arithmetic clue. The two rules below are all you need; everything else is deduction.

Rows and columns

No number may repeat in any row or any column. In a 6×6 puzzle, every row and every column contains each of the numbers 1 through 6 exactly once. (Mathematicians call a grid like this a Latin square.) There are no Sudoku-style boxes — only rows, columns, and cages.

Cages and targets

Every cell belongs to exactly one cage: a connected group of cells marked by a heavy outline. Each cage is labeled with a target number and an operator, such as 11+ or 2÷. The numbers you place in the cage's cells must combine, using that operator, to produce the target.

A number may repeat inside a cage, as long as the repeats sit in different rows and different columns. The row and column rule always applies; the cage adds an arithmetic constraint on top of it.

Operators

Mathdoku uses five cage operators:

Given (no symbol)

A single-cell cage whose value is simply the target. A cage labeled plain 4 holds a 4.

Addition (+)

The cage's values sum to the target. A three-cell 11+ cage might hold 2, 4, and 5.

Subtraction (−)

A two-cell cage whose values differ by the target, in either order. A 3− cage might hold 5 and 2, or 2 and 5.

Multiplication (×)

The cage's values multiply to the target. A three-cell 24× cage might hold 2, 3, and 4.

Division (÷)

A two-cell cage where the larger value divided by the smaller equals the target, in either order. A 2÷ cage might hold 3 and 6.

Subtraction and division cages always have exactly two cells; addition and multiplication cages can be any size from two cells up.

What makes a puzzle fair

A well-made Mathdoku has exactly one solution, reachable by logic alone — no guessing required. That uniqueness is what Mathdoku Designer checks continuously while you author: it re-solves the grid after every edit and reports how many solutions remain.