Daily calcudoku

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 4 addition cages, 3 multiplication cages and 2 division cages.

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Where to start

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

The first moves a careful solver finds:

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

How this grid gives way

Of the 24 cells left to fill after the 12 printed ones, 15 by crossing off what a cell’s row and column already hold until one digit was left; and 9 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