Play Kakuro — Free

What is Kakuro?

Kakuro is a cross-sums logic puzzle — think of it as a crossword built from numbers instead of letters. Rather than filling squares with words, you fill each white run with the digits 1 to 9 so that the run adds up to a target total, called a clue. The clues live in the black cells: a number in the upper-right corner is the sum for the horizontal run running to its right, and a number in the lower-left corner is the sum for the vertical run running below it. The one iron rule is that a digit can never repeat inside the same run, so every answer is a unique little set of numbers hiding behind a single total.

Although Kakuro uses numbers, it is far more about deduction than arithmetic. The addition involved is small and simple; the real work is figuring out which combination of digits a clue can possibly represent, and then narrowing those options using the runs that cross through each cell. Where two runs meet, a cell must satisfy both sums at once, and that overlap is what lets you pin down exact values. Kakuro grew popular in Japan alongside Sudoku and has become a favourite of newspaper puzzle pages worldwide. Every grid on vygam is hand-checked so that its answer is consistent from top to bottom — fill each run correctly and the whole board resolves.

How to Play

A placement is a mistake, and the affected cells turn red, whenever any of the following happens:

• the same digit appears twice inside one run (across or down);
• the digits already entered in a run add up to more than its clue;
• a run is completely filled but does not total its clue exactly;
• you try to use 0 — only the digits 1 to 9 are allowed.

Win the game by filling every white cell so that all across and down runs hit their clues with no repeats. When the last run resolves, a "Solved!" banner appears with your time, and your fastest completion for that puzzle is saved on your device.

Kakuro Tips & Strategy

Kakuro can look daunting, but almost every grid opens up once you learn to read its runs. These four techniques will turn a wall of black cells into a chain of forced moves.

1. Start with unique-sum combinations

   Some clue totals can be built only one way for a given run length, so they hand you the exact digits for free — you only need to work out the order. A two-cell run of 3 is always 1+2; a two-cell run of 17 is always 8+9. Pencil these fixed sets in first, because they anchor everything that crosses them.

   Clue	Cells	Only digits
   3	2	1 + 2
   4	2	1 + 3
   16	2	7 + 9
   17	2	8 + 9
   6	3	1 + 2 + 3
   24	3	7 + 8 + 9

2. Work the crossing cells

   The single most powerful idea in Kakuro is that every white cell belongs to both an across run and a down run. Find a cell where one run allows only a couple of digits and the crossing run allows only a couple more — the answer is whatever number appears on both lists. When you place it, re-check both runs, because each new digit shrinks the options for its neighbours.

3. Use the low and high extremes

   Big and small totals are your friends because they force large or small digits. A three-cell run of 7 can only use low numbers such as 1, 2 and 4, so a 9 is impossible anywhere in it. A three-cell run of 23 must lean on 6, 8 and 9. Rule out the digits a run can never hold, and a crossing cell often collapses to a single choice.

4. Pencil candidates, then eliminate

   When a cell could take more than one value, switch on Notes and jot every candidate. As you confirm digits elsewhere, cross candidates off the cells they clash with. A note left standing alone is a guaranteed answer, and clearing candidates one by one keeps you from guessing. Good Kakuro is never a gamble — there is always a next forced move if you read the sums carefully.

Reading the Clues

The black cells do all the talking in Kakuro. A cell split by a diagonal line can carry two clues at once: the figure above the line, in the upper-right, is the total for the white squares stretching to its right, while the figure below the line, in the lower-left, is the total for the white squares dropping beneath it. A black cell with only one number carries only one run; a plain black cell with no number is simply a spacer that separates runs. Reading the board is just a matter of tracing each white run back to the black cell that owns it.

Because runs are between two and nine cells long and never repeat a digit, the length of a run tells you a lot before you write anything. A two-cell run can hold totals from 3 up to 17; a longer run spreads its total across more digits, so extreme sums become rarer and mid-range sums allow many combinations. Pairing a run's length with its total is how experienced solvers instantly recall which digit sets are even possible — the heart of fast Kakuro.

Kakuro vs Sudoku

Kakuro and Sudoku are cousins: both are pure logic puzzles played on a grid with the digits 1 to 9, and neither rewards guessing. The difference is what the numbers mean. In Sudoku the digits are only symbols and there is no arithmetic at all; you simply avoid repeats in each row, column and box. In Kakuro the digits carry value — every run has a target sum, so you combine the no-repeat rule with light addition to decide what fits. If you enjoy Sudoku's deduction but want a fresh twist, Kakuro adds a satisfying layer of number sense on top of the same clean logic.

Kakuro grids also look different: instead of a fixed 9×9 board, a Kakuro puzzle is an irregular pattern of black and white cells, so no two puzzles feel quite the same shape. That variety, plus the unique-sum shortcuts, is why many solvers keep both games in their daily rotation. On vygam you can jump straight between them — try a quick Kakuro here, then head to Sudoku, Nonogram or Minesweeper when you want a different flavour of logic.

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