Calcudoku for Tuesday, 6 October 2026

The puzzle

Fill every row and every column with the digits 1 to 6, each exactly once, so that the digits in every outlined cage combine to its target with its operation. This one has 6 addition cages, 5 subtraction cages and 2 multiplication cages.

Want to try it before reading on? Play today's grid in Cages — free in the browser, no account needed.

Where to start

5 cells are printed for you: a 2 at row 2, column 5; a 4 at row 3, column 5; a 2 at row 6, column 1; a 1 at row 6, column 2; and a 6 at row 6, column 5. Fill those in first, then let each one rule its digit out of its row and column.

The first moves a careful solver finds:

Cross off what the row and column already rule out, and row 2, column 2 has exactly one candidate left: 4.
Work the 8× cage: with what the board already holds, only 2 can sit in row 3, column 2 and still hit the target.
Cross off what the row and column already rule out, and row 4, column 5 has exactly one candidate left: 1.

How this grid gives way

Of the 31 cells left to fill after the 5 printed ones, 19 by crossing off what a cell’s row and column already hold until one digit was left; and 12 by a cage’s arithmetic leaving only one value that fits. No step needs a guess: every Cages daily is checked to have exactly one solution, reachable by reasoning alone.

The full solution

Show all 31 steps

Cross off what the row and column already rule out, and row 2, column 2 has exactly one candidate left: 4.
Work the 8× cage: with what the board already holds, only 2 can sit in row 3, column 2 and still hit the target.
Cross off what the row and column already rule out, and row 4, column 5 has exactly one candidate left: 1.
Work the 5− cage: with what the board already holds, only 6 can sit in row 4, column 6 and still hit the target.
Cross off what the row and column already rule out, and row 1, column 5 has exactly one candidate left: 3.
Work the 3− cage: with what the board already holds, only 6 can sit in row 1, column 4 and still hit the target.
Cross off what the row and column already rule out, and row 1, column 2 has exactly one candidate left: 5.
Cross off what the row and column already rule out, and row 1, column 3 has exactly one candidate left: 2.
Work the 13+ cage: with what the board already holds, only 6 can sit in row 2, column 3 and still hit the target.
Cross off what the row and column already rule out, and row 4, column 1 has exactly one candidate left: 5.
Work the 11+ cage: with what the board already holds, only 6 can sit in row 3, column 1 and still hit the target.
Cross off what the row and column already rule out, and row 4, column 2 has exactly one candidate left: 3.
Cross off what the row and column already rule out, and row 4, column 3 has exactly one candidate left: 4.
Work the 12+ cage: with what the board already holds, only 5 can sit in row 3, column 3 and still hit the target.
Cross off what the row and column already rule out, and row 4, column 4 has exactly one candidate left: 2.
Cross off what the row and column already rule out, and row 5, column 2 has exactly one candidate left: 6.
Cross off what the row and column already rule out, and row 5, column 3 has exactly one candidate left: 1.
Work the 10+ cage: with what the board already holds, only 3 can sit in row 5, column 1 and still hit the target.
Cross off what the row and column already rule out, and row 2, column 1 has exactly one candidate left: 1.
Work the 3− cage: with what the board already holds, only 4 can sit in row 1, column 1 and still hit the target.
Cross off what the row and column already rule out, and row 1, column 6 has exactly one candidate left: 1.
Cross off what the row and column already rule out, and row 2, column 4 has exactly one candidate left: 3.
Work the 6+ cage: with what the board already holds, only 1 can sit in row 3, column 4 and still hit the target.
Cross off what the row and column already rule out, and row 2, column 6 has exactly one candidate left: 5.
Work the 9+ cage: with what the board already holds, only 3 can sit in row 3, column 6 and still hit the target.
Cross off what the row and column already rule out, and row 5, column 4 has exactly one candidate left: 4.
Work the 20× cage: with what the board already holds, only 5 can sit in row 5, column 5 and still hit the target.
Cross off what the row and column already rule out, and row 5, column 6 has exactly one candidate left: 2.
Work the 2− cage: with what the board already holds, only 4 can sit in row 6, column 6 and still hit the target.
Cross off what the row and column already rule out, and row 6, column 3 has exactly one candidate left: 3.
Cross off what the row and column already rule out, and row 6, column 4 has exactly one candidate left: 5.

Show the finished grid