Kakuro

How to play Kakuro (Cross Sums)

Kakuro, also known as Cross Sums, is a number logic puzzle that feels like a cross between a crossword and Sudoku. Instead of words, you fill the white squares of the grid with the digits 1 to 9 so that every horizontal and vertical run of squares adds up to a target number — its "clue" — while never repeating a digit inside the same run. There is no arithmetic guessing and no luck involved: with careful reasoning every puzzle has one and only one solution, which you can always reach by pure logic. This version comes in three grid sizes, tracks your time and mistakes, and ranks a score for every solve, so you can chase a personal best on Easy, Medium or Hard.

The goal

Your goal is to fill every white square with a digit from 1 to 9 so that two conditions hold everywhere on the board at once. First, each horizontal "across" run and each vertical "down" run of white squares must add up exactly to the clue printed in the black cell just before it. Second, a digit may never appear twice within the same run. When every run satisfies both conditions the puzzle is solved. Because 0 is never used and digits cannot repeat in a run, a run can be at most nine squares long.

The board

The board is a grid of black and white squares. White squares are the ones you fill in. Black squares are walls that either block off part of the grid or carry the clues. A "run" (sometimes called an entry) is a straight line of two or more white squares with no black square between them; each run runs left-to-right (across) or top-to-bottom (down). Every white square belongs to exactly one across run and one down run, so each digit you write is constrained in two directions at the same time. That double constraint is what makes Kakuro solvable by logic alone.

Reading the clues

The clues live in the black cells and are split by a diagonal line. The number in the top-right, above the diagonal, is the "across" clue: it is the required sum of the run of white squares stretching to the right of that black cell. The number in the bottom-left, below the diagonal, is the "down" clue: it is the required sum of the run of white squares heading downward from that black cell. A black cell can carry an across clue, a down clue, both, or neither. For example, a black cell showing 16 in the top-right means the white squares immediately to its right must add up to 16.

The rules

• Fill white squares only with the digits 1 to 9. Zero is never used, and black squares are never filled.
• Every across run must add up to the across clue in the black cell to its left; every down run must add up to the down clue in the black cell above it.
• No digit may repeat within a single run. It is perfectly fine, though, for the same digit to appear in a crossing run — the no-repeat rule applies only along one straight run at a time.
• The board turns a square red when its across or down run goes over the target, or when a digit is repeated in a run, so you get instant feedback on an impossible move.
• To make each puzzle solvable by pure deduction from the very first move, a few white squares start already filled with fixed "starter" numbers that you cannot change. Easier grids reveal a little more help than harder ones.

Magic combinations

The key technique in Kakuro is spotting which sets of digits can possibly fill a run of a given length and sum. Some length-and-sum pairs allow only one set of digits (in some order); these "magic" combinations are the fastest way into a puzzle. The Combinations helper in the game lists every set that still fits a selected run, but learning a handful by heart is worth it:

• Two squares summing to 3 must be 1 and 2; summing to 4 must be 1 and 3; summing to 16 must be 7 and 9; summing to 17 must be 8 and 9. Each of these has only one possible pair.
• Three squares summing to 6 must be 1, 2 and 3; summing to 7 must be 1, 2 and 4; summing to 23 must be 6, 8 and 9; summing to 24 must be 7, 8 and 9.
• The smallest and largest sums for a run of a given length are the most useful, because they force a unique set. When two crossing runs each force a set, the shared square must hold a digit common to both — often pinning it down exactly.
• A run of nine squares must contain every digit 1 to 9 exactly once and always sums to 45, so a full row or column is completely determined as a set (only the order is left to work out).

Controls

Tap a white square to select it, then tap a number on the pad (or press a key from 1 to 9) to write that digit. Tap the same digit again, press 0, or use the erase key to clear the square. On a computer you can select a square and type; on a phone everything works by tapping. Turn on the Combinations helper to see, for the selected square, the digit sets that can still complete each of its runs. Use New puzzle to generate a fresh grid, and the Level menu to switch between Easy, Medium and Hard.

Winning

You win the moment every across run and every down run adds up to its clue with no repeated digits — in other words, when the whole grid is correctly filled. The timer stops, a win banner appears, and your score is calculated and submitted to the leaderboard. Because each puzzle has a single unique solution, there is exactly one correct grid to reach; you never have to guess, and a careful solver can always finish.

Strategy tips

• Start with the runs that have a forced set — very small or very large sums, and short runs. A two-square run summing to 17, for instance, immediately tells you the squares are 8 and 9 in some order.
• Look at crossings. When a square sits on both a forced across run and a forced down run, the answer is the digit those two sets share. This is how most Kakuro squares are cracked.
• Use the starter numbers. Each fixed square not only fills itself but also constrains its across and down runs, shrinking the possibilities for their other squares.
• Pencil in candidates mentally or use the Combinations helper, then eliminate. If a digit would make a run exceed its clue or duplicate an existing digit, it is out.
• Work the low-mistake way: the score rewards speed but punishes wrong entries heavily, so it usually pays to be sure of a square before you commit rather than filling in on a hunch.

Frequently asked questions