How to play Kakuro
The rules take a minute. The habits that make a first grid finishable take about ten, and they are the rest of this page.
The rules, in full
A Kakuro grid is part white squares and part clue blocks. Every unbroken line of white squares, across or down, is a run. Each run has a clue: the number its digits must add up to.
Only the digits one to nine are used — there is never a zero and never a ten. Within a single run no digit may repeat. Across different runs digits repeat freely, which is the rule people most often get backwards coming from Sudoku, where a digit appears once per row, column and box.
The clue blocks are split corner to corner. The number above the diagonal is the clue for the run running to the right; the number below it is for the run running down. A block with only one number governs only one run, and a plain block with no numbers is just a wall.
That is everything. There is no hidden rule about grid symmetry, no constraint linking one run to another beyond the squares they share, and a correctly made puzzle needs no guessing.
The first three moves worth knowing
Learn the sums that can only be written one way. Three across two squares must be one and two. Four across two must be one and three. Sixteen across two is seven and nine, and seventeen is eight and nine. Six across three is one, two and three; twenty-four across three is seven, eight and nine. Those six facts open more grids than anything else you can memorise.
Look for where two of them cross. If a square sits on a run that must contain seven and nine, and also on a run that must contain one and two, there is nothing that can go there — so one of those runs is not what you thought. If it sits on a run needing eight or nine and another needing seven or nine, it is a nine.
And subtract. When a run has one square left, its digit is the clue minus the digits already written. That is the least interesting move in the game and it will place more squares for you than any clever one.
What beginners get wrong
Assuming a digit cannot repeat in a column. It cannot repeat within a run, and a column is usually several runs separated by blocks. Two sevens in one column are perfectly legal as long as a block sits between them.
Starting in the middle. Long runs with middling clues are the least informative squares on the grid; the corners and the short runs are where the information is. Work from the edges inward.
And treating the diagonal as decoration. Reading an across clue as a down clue produces a grid that seems to contradict itself for reasons you will not find, and it is by far the commonest source of a wasted half hour.
Common questions
- Can a digit repeat in a Kakuro column?
- Yes, as long as a block separates the two occurrences. The no-repeat rule applies within a single run, not down a whole column — which is the opposite of Sudoku.
- What do the two numbers in a Kakuro block mean?
- The one above the diagonal is the total for the run going right; the one below is for the run going down. A block with a single number governs only one run.
- Is zero ever used in Kakuro?
- Never. Only the digits one to nine appear in the white squares, which is why the smallest possible two-square clue is three and the largest is seventeen.
- Do I ever have to guess at Kakuro?
- Not on a well-made puzzle. Harder grids may need you to follow a digit and see whether it contradicts, but that always resolves — it is a test, not a hope.
Check this before you rely on it. This tool is provided free and without warranty, and its results are not professional advice.