Kakuro

How to play

Kakuro (also called cross-sums) is played on a grid of white cells and blocked cells. Every unbroken run of white cells, reading across or down, carries a small number — the target that run's digits must add up to. Tap a white cell to select it, then tap a digit from 1 to 9 below the board to fill it in. The catch: the digits within any single run must all be different from each other, the same rule that makes Sudoku work. The puzzle is solved once every run's digits sum to its target with no repeats.

Working out the digits

A two-cell run is the easiest place to start, since a target of, say, 4 can only be made from two different digits 1-9 in one way: 1 and 3 (not 2 and 2 — repeats aren't allowed). A target of 16 across two cells is just as narrow: only 7 and 9 will do. The tighter a run's target is against its length, the fewer combinations are possible, so look for those first.

Where a run crosses another, the shared cell has to satisfy both at once — narrowing down one run's possible digits often narrows the crossing run too, the same back-and-forth that solving a nonogram or a crossword relies on.

Turn on "Highlight mistakes" below the board if you'd like a filled-in digit marked in red the moment it doesn't belong in the finished solution — useful while you're still getting a feel for the combinations, and easy to turn back off once you'd rather reason it out yourself.