Calcudoku: rules and how to play

Goal of the game

Complete a number grid while satisfying every arithmetic cage. Each cell must work both in its row and column and in its cage.

Rules

• On an N×N grid, each row and column contains 1 through N exactly once. There are no Sudoku boxes.
• A cage gives a target and an operation. Add or multiply all its numbers to reach that target.
• Subtraction and division cages have two cells: subtract the smaller from the larger, or divide the larger by the smaller. Division must be exact.
• A one-cell cage gives its value directly. Repetition within a cage is allowed only when it does not repeat a number in a row or column. There is no extra cage-wide no-repeat rule.

A small example, step by step

1. On a 4×4 grid, a two-cell cage in one row has target 3+.
2. The only possible numbers are 1 and 2. Their order is still undecided.
3. If the first cell’s column already contains 1, that cell must be 2 and the other must be 1.
4. For a separate 2÷ cage on this size, the possible pairs are 1 with 2 or 2 with 4; the crossing rows and columns decide which survives.

Beginner deductions

• Start with one-cell cages and nearly complete rows or columns.
• List the small combinations for a cage, then remove combinations incompatible with row and column digits.
• Keep both orders until a crossing excludes one. A forced combination is not always a forced position.

Common mistakes

• Do not treat 3− as left cell minus right cell: the larger value comes first.
• Do not forbid all repeated cage values as in Killer Sudoku.
• Do not use fractions or add numbers when the cage asks for multiplication.