Calcudoku for Sunday, 30 August 2026

The puzzle

Fill every row and every column with the digits 1 to 8, each exactly once, so that the digits in every outlined cage combine to its target with its operation. This one has 8 addition cages, 6 subtraction cages and 10 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

9 cells are printed for you: a 2 at row 1, column 1; a 2 at row 4, column 4; a 2 at row 5, column 6; a 5 at row 6, column 4; a 6 at row 6, column 6; a 3 at row 8, column 2; a 4 at row 8, column 3; a 2 at row 8, column 7; and a 7 at row 8, column 8. 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 8, column 1 has exactly one candidate left: 1.
Work the 5+ cage: with what the board already holds, only 4 can sit in row 7, column 1 and still hit the target.
Cross off what the row and column already rule out, and row 6, column 1 has exactly one candidate left: 3.

How this grid gives way

Of the 55 cells left to fill after the 9 printed ones, 28 by a cage’s arithmetic leaving only one value that fits; 25 by crossing off what a cell’s row and column already hold until one digit was left; and 2 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 55 steps

Cross off what the row and column already rule out, and row 8, column 1 has exactly one candidate left: 1.
Work the 5+ cage: with what the board already holds, only 4 can sit in row 7, column 1 and still hit the target.
Cross off what the row and column already rule out, and row 6, column 1 has exactly one candidate left: 3.
Work the 112× cage: with what the board already holds, only 2 can sit in row 2, column 3 and still hit the target.
Cross off what the row and column already rule out, and row 6, column 2 has exactly one candidate left: 2.
Work the 6× cage: with what the board already holds, only 1 can sit in row 6, column 3 and still hit the target.
Cross off what the row and column already rule out, and row 6, column 8 has exactly one candidate left: 8.
Work the 6− cage: with what the board already holds, only 2 can sit in row 7, column 8 and still hit the target.
Cross off what the row and column already rule out, and row 6, column 7 has exactly one candidate left: 4.
Cross off what the row and column already rule out, and row 6, column 5 has exactly one candidate left: 7.
Somewhere in this line the 7 must go — and row 2, column 6 is the only cell that can still take it.
Work the 10+ cage: with what the board already holds, only 3 can sit in row 2, column 7 and still hit the target.
Somewhere in this line the 3 must go — and row 1, column 6 is the only cell that can still take it.
Work the 3− cage: with what the board already holds, only 6 can sit in row 1, 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: 8.
Work the 96× cage: with what the board already holds, only 3 can sit in row 5, column 8 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: 1.
Work the 3× cage: with what the board already holds, only 3 can sit in row 4, column 5 and still hit the target.
Work the 13+ cage: with what the board already holds, only 7 can sit in row 4, column 7 and still hit the target.
Work the 13+ cage: with what the board already holds, only 6 can sit in row 4, column 8 and still hit the target.
Work the 168× cage: with what the board already holds, only 4 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 6 has exactly one candidate left: 4.
Work the 4× cage: with what the board already holds, only 1 can sit in row 4, column 6 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: 5.
Work the 6+ cage: with what the board already holds, only 1 can sit in row 7, column 7 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: 5.
Work the 4− cage: with what the board already holds, only 1 can sit in row 3, column 8 and still hit the target.
Cross off what the row and column already rule out, and row 8, column 4 has exactly one candidate left: 6.
Work the 9+ cage: with what the board already holds, only 3 can sit in row 7, column 4 and still hit the target.
Cross off what the row and column already rule out, and row 8, column 5 has exactly one candidate left: 5.
Work the 40× cage: with what the board already holds, only 8 can sit in row 8, column 6 and still hit the target.
Work the 13+ cage: with what the board already holds, only 1 can sit in row 2, column 4 and still hit the target.
Work the 30× cage: with what the board already holds, only 1 can sit in row 1, column 2 and still hit the target.
Work the 10+ cage: with what the board already holds, only 8 can sit in row 3, column 4 and still hit the target.
Work the 10+ cage: with what the board already holds, only 2 can sit in row 3, column 5 and still hit the target.
Cross off what the row and column already rule out, and row 1, column 4 has exactly one candidate left: 7.
Work the 112× cage: with what the board already holds, only 8 can sit in row 1, column 3 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: 4.
Work the 13+ cage: with what the board already holds, only 8 can sit in row 2, column 5 and still hit the target.
Cross off what the row and column already rule out, and row 1, column 8 has exactly one candidate left: 5.
Work the 20× cage: with what the board already holds, only 4 can sit in row 2, column 8 and still hit the target.
Cross off what the row and column already rule out, and row 4, column 3 has exactly one candidate left: 5.
Cross off what the row and column already rule out, and row 3, column 3 has exactly one candidate left: 3.
Cross off what the row and column already rule out, and row 4, column 1 has exactly one candidate left: 8.
Work the 1− cage: with what the board already holds, only 7 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 1 has exactly one candidate left: 6.
Work the 168× cage: with what the board already holds, only 7 can sit in row 3, column 2 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: 5.
Work the 30× cage: with what the board already holds, only 6 can sit in row 2, column 2 and still hit the target.
Cross off what the row and column already rule out, and row 5, column 2 has exactly one candidate left: 5.
Cross off what the row and column already rule out, and row 5, column 3 has exactly one candidate left: 6.
Work the 15+ cage: with what the board already holds, only 4 can sit in row 5, column 4 and still hit the target.
Cross off what the row and column already rule out, and row 7, column 2 has exactly one candidate left: 8.
Work the 56× cage: with what the board already holds, only 7 can sit in row 7, column 3 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: 6.

Show the finished grid