Kakuro: The Cross-Sum Puzzle Worth Learning 🔢

The rules

You have a grid of black and white cells. Black cells carry clues — a number in the top-right for the run of white cells to its right, a number in the bottom-left for the run going down.

Fill every white cell with a digit from 1 to 9 so that:

• each run of white cells adds up to its clue, and
• no digit repeats within a run.

That second rule is the engine of the whole game. Zero is never used.

The magic combinations

Because digits can't repeat, some clues have exactly one possible set of digits. These are the footholds, and knowing about six of them changes the game completely:

Clue	Cells	Only possible digits
3	2	1, 2
4	2	1, 3
16	2	7, 9
17	2	8, 9
6	3	1, 2, 3
7	3	1, 2, 4
23	3	6, 8, 9
24	3	7, 8, 9
10	4	1, 2, 3, 4
30	4	6, 7, 8, 9

The pattern is simple enough to reconstruct rather than memorise: the smallest and largest few sums for any run length are forced, because there is only one way to be that extreme.

Working the intersections

Every foothold is only useful where two runs cross. Suppose an across-run of 17 in two cells (so {8,9}) meets a down-run of 4 in two cells (so {1,3}). The shared cell has to be in both sets — and the sets don't overlap, which means you've proved that layout impossible and can look elsewhere.

More usefully, when a 16-in-2 ({7,9}) crosses a 6-in-3 ({1,2,3}), the intersection is empty as well. When a 16-in-2 crosses a 23-in-3 ({6,8,9}), the shared cell must be 9. That is the whole game: two constraint sets, one shared cell, and whatever survives the intersection.

From there you use the same eliminations you'd use in Sudoku. A digit that can only go in one cell of a run is placed, and a pair of cells that share the same two candidates locks those digits out of the rest of the run.

About our version

99 levels on a curve that starts at 5×5 and grows to 10×10. Every level is generated with a solver in the loop and verified to have exactly one solution — when the generator finds a board with two, it promotes a differing cell into a clue and re-checks, which kills the rival solution rather than throwing the board away.

Notes for candidate digits, unlimited undo, and hints. Six languages including Arabic with a right-to-left layout.

It runs in your browser, works offline once loaded, needs no account, and costs nothing.

Questions people actually ask

Is Kakuro harder than Sudoku?
Steeper to start, yes, because you need the sum combinations before anything opens up. Once you have those, a mid-difficulty Kakuro plays at about the same level as a hard Sudoku.

Can a digit repeat in Kakuro?
Not within a single run. It can absolutely appear again in a different run, including one that crosses it — the no-repeat rule is per run, not per row of the whole grid.

Do I need to be good at arithmetic?
Barely. The sums are small and you'll end up recognising combinations rather than adding. It's a logic puzzle wearing arithmetic as a costume.

Keep reading

• Sudoku Online: How to Play and How to Get Faster 🔢 — Four difficulties, pencil marks, and a hint that teaches instead of just filling a square. Plus the three techniques that get you past Easy.
• Cages: Killer Sudoku Explained (and How to Open One) 🔢 — Sudoku with sums bolted on. The cages look like extra work but they're a gift — they let you start deducing before a single digit is on the board.
• Logic Puzzle Games: A Guide to the 12 in Go Brain 🧠 — Sudoku, Kakuro, Nonogram, Crowns and eight more. What separates a real deduction puzzle from a guessing game, and which to start with.