Calcudoku for Thursday, 20 August 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 6 addition cages and 9 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 7 at row 1, column 1; a 3 at row 1, column 5; a 4 at row 4, column 4; a 6 at row 7, column 1; and a 2 at row 7, column 4. Fill those in first, then let each one rule its digit out of its row and column.

The first moves a careful solver finds:

Somewhere in this line the 1 must go — and row 1, column 2 is the only cell that can still take it.
Somewhere in this line the 6 must go — and row 1, column 4 is the only cell that can still take it.
Cross off what the row and column already rule out, and row 3, column 4 has exactly one candidate left: 5.

How this grid gives way

Of the 44 cells left to fill after the 5 printed ones, 22 by crossing off what a cell’s row and column already hold until one digit was left; 18 by a cage’s arithmetic leaving only one value that fits; and 4 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

Somewhere in this line the 1 must go — and row 1, column 2 is the only cell that can still take it.
Somewhere in this line the 6 must go — and row 1, column 4 is the only cell that can still take it.
Cross off what the row and column already rule out, and row 3, column 4 has exactly one candidate left: 5.
Cross off what the row and column already rule out, and row 2, column 4 has exactly one candidate left: 7.
Work the 15+ cage: with what the board already holds, only 2 can sit in row 1, column 3 and still hit the target.
Work the 40× cage: with what the board already holds, only 2 can sit in row 2, column 6 and still hit the target.
Work the 11+ cage: with what the board already holds, only 7 can sit in row 5, column 3 and still hit the target.
Somewhere in this line the 5 must go — and row 1, column 7 is the only cell that can still take it.
Work the 40× cage: with what the board already holds, only 4 can sit in row 1, column 6 and still hit the target.
Somewhere in this line the 3 must go — and row 2, column 1 is the only cell that can still take it.
Work the 12× cage: with what the board already holds, only 4 can sit in row 2, column 2 and still hit the target.
Cross off what the row and column already rule out, and row 2, column 3 has exactly one candidate left: 5.
Cross off what the row and column already rule out, and row 2, column 5 has exactly one candidate left: 6.
Work the 120× cage: with what the board already holds, only 4 can sit in row 3, column 5 and still hit the target.
Cross off what the row and column already rule out, and row 2, column 7 has exactly one candidate left: 1.
Cross off what the row and column already rule out, and row 4, column 5 has exactly one candidate left: 2.
Cross off what the row and column already rule out, and row 7, column 2 has exactly one candidate left: 5.
Work the 15× cage: with what the board already holds, only 3 can sit in row 7, column 3 and still hit the target.
Work the 10+ cage: with what the board already holds, only 1 can sit in row 3, column 1 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: 6.
Work the 30× cage: with what the board already holds, only 1 can sit in row 4, 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.
Cross off what the row and column already rule out, and row 6, column 3 has exactly one candidate left: 4.
Cross off what the row and column already rule out, and row 6, column 1 has exactly one candidate left: 2.
Work the 11+ cage: with what the board already holds, only 4 can sit in row 5, column 1 and still hit the target.
Cross off what the row and column already rule out, and row 3, column 7 has exactly one candidate left: 3.
Work the 21× cage: with what the board already holds, only 7 can sit in row 3, column 6 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: 2.
Work the 10+ 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 4, column 6 has exactly one candidate left: 3.
Work the 36× cage: with what the board already holds, only 6 can sit in row 4, column 7 and still hit the target.
Cross off what the row and column already rule out, and row 5, column 7 has exactly one candidate left: 2.
Cross off what the row and column already rule out, and row 6, column 7 has exactly one candidate left: 7.
Work the 56× cage: with what the board already holds, only 4 can sit in row 7, column 7 and still hit the target.
Cross off what the row and column already rule out, and row 7, column 5 has exactly one candidate left: 7.
Cross off what the row and column already rule out, and row 6, column 6 has exactly one candidate left: 5.
Work the 13+ cage: with what the board already holds, only 1 can sit in row 7, column 6 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: 6.
Cross off what the row and column already rule out, and row 5, column 2 has exactly one candidate left: 3.
Work the 13+ cage: with what the board already holds, only 6 can sit in row 6, column 2 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: 1.
Work the 11+ 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 5, column 5 has exactly one candidate left: 5.
Work the 30× cage: with what the board already holds, only 1 can sit in row 6, column 5 and still hit the target.

Show the finished grid