Calcudoku for Thursday, 1 October 2026

The puzzle

Fill every row and every column with the digits 1 to 7, each exactly once, so that the digits in every outlined cage combine to its target with its operation. This one has 10 addition cages, 6 subtraction cages, 2 multiplication cages and 1 division cage.

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 5 at row 3, column 1; a 4 at row 3, column 5; a 5 at row 4, column 6; a 4 at row 5, column 6; and a 1 at row 7, column 2. 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 1, column 6 has exactly one candidate left: 7.
Work the 12+ cage: with what the board already holds, only 5 can sit in row 1, column 7 and still hit the target.
Work the 6+ cage: with what the board already holds, only 2 can sit in row 3, column 4 and still hit the target.

How this grid gives way

Of the 44 cells left to fill after the 5 printed ones, 23 by a cage’s arithmetic leaving only one value that fits; 18 by crossing off what a cell’s row and column already hold until one digit was left; and 3 by finding the one place left in a line where a digit could still go. No step needs a guess: every Cages daily is checked to have exactly one solution, reachable by reasoning alone.

The full solution

Show all 44 steps

Cross off what the row and column already rule out, and row 1, column 6 has exactly one candidate left: 7.
Work the 12+ cage: with what the board already holds, only 5 can sit in row 1, column 7 and still hit the target.
Work the 6+ cage: with what the board already holds, only 2 can sit in row 3, column 4 and still hit the target.
Work the 6+ cage: with what the board already holds, only 4 can sit in row 4, column 4 and still hit the target.
Somewhere in this line the 2 must go — and row 2, column 1 is the only cell that can still take it.
Work the 3− cage: with what the board already holds, only 5 can sit in row 2, column 2 and still hit the target.
Work the 8+ cage: with what the board already holds, only 1 can sit in row 6, column 1 and still hit the target.
Somewhere in this line the 2 must go — and row 1, column 2 is the only cell that can still take it.
Work the 2− 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 7, column 1 has exactly one candidate left: 3.
Work the 8+ cage: with what the board already holds, only 4 can sit in row 6, column 2 and still hit the target.
Work the 16+ cage: with what the board already holds, only 3 can sit in row 5, column 2 and still hit the target.
Work the 11+ cage: with what the board already holds, only 5 can sit in row 7, column 5 and still hit the target.
Cross off what the row and column already rule out, and row 7, column 6 has exactly one candidate left: 2.
Work the 11+ cage: with what the board already holds, only 4 can sit in row 7, column 7 and still hit the target.
Work the 18+ cage: with what the board already holds, only 5 can sit in row 6, column 3 and still hit the target.
Work the 15+ cage: with what the board already holds, only 6 can sit in row 6, column 6 and still hit the target.
Somewhere in this line the 4 must go — and row 2, column 3 is the only cell that can still take it.
Cross off what the row and column already rule out, and row 1, column 3 has exactly one candidate left: 1.
Cross off what the row and column already rule out, and row 1, column 4 has exactly one candidate left: 6.
Work the 6÷ cage: with what the board already holds, only 1 can sit in row 2, column 4 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 2, column 5 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: 3.
Cross off what the row and column already rule out, and row 2, column 7 has exactly one candidate left: 7.
Work the 21× cage: with what the board already holds, only 3 can sit in row 3, column 7 and still hit the target.
Cross off what the row and column already rule out, and row 3, column 6 has exactly one candidate left: 1.
Cross off what the row and column already rule out, and row 5, column 4 has exactly one candidate left: 5.
Cross off what the row and column already rule out, and row 4, column 5 has exactly one candidate left: 2.
Work the 2× cage: with what the board already holds, only 1 can sit in row 5, column 5 and still hit the target.
Cross off what the row and column already rule out, and row 4, column 7 has exactly one candidate left: 1.
Work the 5− cage: with what the board already holds, only 6 can sit in row 5, column 7 and still hit the target.
Cross off what the row and column already rule out, and row 5, column 1 has exactly one candidate left: 7.
Work the 16+ cage: with what the board already holds, only 6 can sit in row 4, column 1 and still hit the target.
Cross off what the row and column already rule out, and row 3, column 2 has exactly one candidate left: 6.
Work the 13+ cage: with what the board already holds, only 7 can sit in row 4, column 2 and still hit the target.
Cross off what the row and column already rule out, and row 3, column 3 has exactly one candidate left: 7.
Work the 10+ cage: with what the board already holds, only 3 can sit in row 4, column 3 and still hit the target.
Cross off what the row and column already rule out, and row 5, column 3 has exactly one candidate left: 2.
Work the 10+ cage: with what the board already holds, only 3 can sit in row 6, column 4 and still hit the target.
Cross off what the row and column already rule out, and row 6, column 5 has exactly one candidate left: 7.
Work the 15+ cage: with what the board already holds, only 2 can sit in row 6, column 7 and still hit the target.
Cross off what the row and column already rule out, and row 7, column 3 has exactly one candidate left: 6.
Work the 18+ cage: with what the board already holds, only 7 can sit in row 7, column 4 and still hit the target.

Show the finished grid