Sums

Puzzle · plays in your browser, no download

Digits one to nine. Every run adds up to the number written beside it, and no digit repeats inside a run.

Where it comes from

Kakuro, cross sums, the crossword where the clues are totals. It is the one puzzle in this collection that really is arithmetic, and the arithmetic is tiny — nothing in it is harder than adding up to forty-five. The difficulty is all in which sums have only one way of being made.

How to play

Fill the white squares with digits one to nine. Tap a square, then a number.
Each run has to add up to the number written in the black square that opens it: top right for the row, bottom left for the column.
Every puzzle here can be solved: the sums are read off a solution that already exists, not invented and hoped for.

What makes this one different

Two squares adding to three can only be one and two, and the run crossing them decides which goes where — that is the whole puzzle, and it never needs a guess. A run turns red only when it is full and still wrong, so a half-finished run tells you nothing. And if you find a different solution that works, you win: the game checks the sums, not the answer it had in mind.

▶ Play Sums