Calcudoku for Thursday, 10 September 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 9 addition cages, 4 subtraction cages, 5 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

4 cells are printed for you: a 3 at row 1, column 3; a 5 at row 1, column 6; a 7 at row 1, column 7; and a 2 at row 7, column 7. Fill those in first, then let each one rule its digit out of its row and column.

The first moves a careful solver finds:

Work the 252× cage: with what the board already holds, only 6 can sit in row 2, column 2 and still hit the target.
Work the 252× cage: with what the board already holds, only 7 can sit in row 2, column 3 and still hit the target.
Work the 252× cage: with what the board already holds, only 6 can sit in row 3, column 3 and still hit the target.

How this grid gives way

Of the 45 cells left to fill after the 4 printed ones, 23 by a cage’s arithmetic leaving only one value that fits; 20 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 45 steps

Work the 252× cage: with what the board already holds, only 6 can sit in row 2, column 2 and still hit the target.
Work the 252× cage: with what the board already holds, only 7 can sit in row 2, column 3 and still hit the target.
Work the 252× cage: with what the board already holds, only 6 can sit in row 3, column 3 and still hit the target.
Work the 30× cage: with what the board already holds, only 5 can sit in row 6, column 7 and still hit the target.
Work the 10+ 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 4, column 1 has exactly one candidate left: 7.
Work the 13+ cage: with what the board already holds, only 6 can sit in row 5, column 1 and still hit the target.
Work the 70× cage: with what the board already holds, only 7 can sit in row 3, column 4 and still hit the target.
Work the 16+ 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: 7.
Work the 16+ cage: with what the board already holds, only 4 can sit in row 5, column 7 and still hit the target.
Somewhere in this line the 1 must go — and row 1, column 4 is the only cell that can still take it.
Work the 7+ cage: with what the board already holds, only 6 can sit in row 1, column 5 and still hit the target.
Somewhere in this line the 5 must go — and row 2, column 1 is the only cell that can still take it.
Work the 5× 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 2, column 4 has exactly one candidate left: 2.
Work the 70× cage: with what the board already holds, only 5 can sit in row 4, column 4 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.
Work the 10+ 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 5, column 4 has exactly one candidate left: 3.
Cross off what the row and column already rule out, and row 7, column 1 has exactly one candidate left: 3.
Work the 4− cage: with what the board already holds, only 7 can sit in row 7, column 2 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 7÷ cage: with what the board already holds, only 1 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: 6.
Work the 30× cage: with what the board already holds, only 1 can sit in row 6, column 6 and still hit the target.
Cross off what the row and column already rule out, and row 7, column 4 has exactly one candidate left: 4.
Work the 13+ cage: with what the board already holds, only 6 can sit in row 6, column 4 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: 5.
Cross off what the row and column already rule out, and row 6, column 1 has exactly one candidate left: 2.
Work the 5+ cage: with what the board already holds, only 3 can sit in row 6, column 2 and still hit the target.
Cross off what the row and column already rule out, and row 1, column 1 has exactly one candidate left: 4.
Work the 6+ cage: with what the board already holds, only 2 can sit in row 1, 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: 1.
Cross off what the row and column already rule out, and row 4, column 2 has exactly one candidate left: 4.
Work the 10+ cage: with what the board already holds, only 5 can sit in row 3, 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 8× cage: with what the board already holds, only 2 can sit in row 4, column 6 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.
Work the 7+ cage: with what the board already holds, only 4 can sit in row 2, column 5 and still hit the target.
Cross off what the row and column already rule out, and row 3, column 5 has exactly one candidate left: 2.
Cross off what the row and column already rule out, and row 4, column 3 has exactly one candidate left: 1.
Work the 1− cage: with what the board already holds, only 2 can sit in row 5, column 3 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: 3.
Cross off what the row and column already rule out, and row 6, column 3 has exactly one candidate left: 4.

Show the finished grid