What is Calcudoku?

Calcudoku is the maths-flavoured cousin of sudoku, also known as KenKen or MathDoku. The grid is small — 4×4 or 6×6 — and there are no given digits at all: every clue comes from the outlined “cages” and the little calculations in their corners.

The rules

Fill the grid so that every row and every column contains each digit exactly once: 1 to 4 on a 4×4 grid, 1 to 6 on a 6×6 — like a sudoku without boxes. On top of that the grid is divided into cages, connected groups of cells marked by thick borders, and the label in a cage’s corner tells you what its digits must produce.

The cage labels read like this:

• 7+ — the digits in the cage add up to 7
• 8× — they multiply to 8
• 3− — two cells whose difference is 3
• 2÷ — two cells where the larger divided by the smaller gives 2
• 4 (no sign) — a single cell that simply contains 4

One subtlety: a digit may appear twice inside the same cage, as long as the two cells don’t share a row or column. Rows and columns are the only uniqueness rules.

A solved example

A solved 4×4 calcudoku — check each cage against its label.

How to get started

• Fill the single-cell cages first — they are free digits, and every placed digit constrains its whole row and column.
• Look for extreme targets. On a 6×6, a two-cell cage marked 11+ can only be 5 and 6; a three-cell 6+ can only be 1, 2 and 3; a large product like 90× factors only one way.
• Use pencil marks exactly as in sudoku: note the few possible digits in a cell and cross them off as rows, columns and cage arithmetic rule them out.
• Difference and division cages always have two cells — list their possible pairs and test each against the crossing row and column.