Daily calcudoku

The puzzle

Fill every row and every column with the digits 1 to 5, each exactly once, so that the digits in every outlined cage combine to its target with its operation. This one has 2 addition cages, 4 subtraction cages, 3 multiplication cages and 2 division cages.

Want to try it before reading on? Play today's grid in Cages — free in the browser, no account needed.

Where to start

2 cells are printed for you: a 1 at row 1, column 3; and a 5 at row 4, column 5. 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. Somewhere in this line the 4 must go — and row 1, column 2 is the only cell that can still take it.
2. Cross off what the row and column already rule out, and row 1, column 5 has exactly one candidate left: 2.
3. Work the 6+ cage: with what the board already holds, only 4 can sit in row 2, column 5 and still hit the target.

How this grid gives way

Of the 23 cells left to fill after the 2 printed ones, 14 by crossing off what a cell’s row and column already hold until one digit was left; 8 by a cage’s arithmetic leaving only one value that fits; and 1 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