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Guide

The Kakuro Game, Explained

A crossword where the clues are sums — one rule, endless logic.

What is the Kakuro game?

Kakuro is a logic puzzle played on a crossword-style grid of black and white cells. Black clue cells carry a diagonal slash with up to two numbers: the top number is the sum of the horizontal run of white cells to the right, the bottom number the sum of the vertical run below. You fill every white cell with a digit from 1 to 9 so each run totals its clue — and no digit repeats within a run.

That single no-repeat rule is what turns arithmetic into deduction. A clue of 17 over two cells cannot be 9+8 and 8+9 in either order until the crossing clues have their say; often only one arrangement survives. Well-made Kakuro — including every board on this site — has exactly one solution, reachable without guessing.

A short history: from Cross Sums to Kakuro

The puzzle was invented in America, first published by Dell in 1966 under the name Cross Sums (sometimes Cross Addition). Japanese publishers imported it in the 1980s, where it took the name kasan kurosu — 'addition cross' — later contracted to Kakuro, and became one of Japan's most popular pencil puzzles alongside sudoku.

When sudoku swept the world in 2005, Kakuro followed as 'the next Japanese puzzle', appearing in major newspapers and dozens of books. The names still coexist: American magazines kept Cross Sums for decades, while Kakuro is the standard name online. Our [Cross Sums page](/cross-sums) covers the original-name lineage in more depth.

Playing Kakuro online, free

Everything here is free in the browser: a shared daily Kakuro with streaks and a permanent archive, plus an unlimited library across five grid sizes from 4 × 4 to 9 × 11, graded easy to hard by a technique-replay solver.

The player is built around the way Kakuro is actually solved: tap any clue for a live list of its remaining digit combinations, pencil-mark candidates, and let the automatic checker flag contradictions. The full combination tables — including every magic block — live on the [combinations reference](/combinations).

Frequently asked questions

Is Kakuro harder than sudoku?
They exercise different muscles. Sudoku is pure placement logic; Kakuro adds arithmetic, so you juggle sums and uniqueness at once. Small Kakuro boards are gentler than most sudoku, while large boards with long runs can be considerably deeper. Combination knowledge — knowing that 24-in-three must be 7+8+9 — closes most of the gap.
Does Kakuro use the digit 0?
No. Kakuro uses only the digits 1 through 9. That is why run sums range from 3 (two cells: 1+2) up to 45 (nine cells using every digit once), and why the no-repeat rule caps runs at nine cells.
Can every Kakuro be solved by logic alone?
A properly constructed Kakuro has exactly one solution and never needs guessing. Every puzzle published on this site is machine-verified for a unique solution before release, and its difficulty label records which techniques the solve genuinely requires.

Play Kakuro now →