Kakuro Solver, Step by Step
First tap squares to make them black or white. Then switch to clues and tap each black square to type its sums.
How to use the kakuro solver
Set the width and height, then in Black squares tap every square that is black on your puzzle. Switch to Clues and tap each black square that has numbers: type the sum for the run to its right and the sum for the run below it. Leave a box empty if there is no run that way. Then press Explain the next step: the solver fills in the next number that is certain, highlights the run that proves it, and says why. Show the answer fills it all at once and says whether the solution is the only one.
How to solve kakuro, step by step
Learn the runs with one answer. No number may repeat in a run, so some sums can only be made one way: 3 in two squares is 1 + 2, 4 is 1 + 3, 16 is 7 + 9 and 17 is 8 + 9; in three squares 6 is 1 + 2 + 3 and 24 is 7 + 8 + 9. Those are where every kakuro starts.
Cross the runs. Every white square sits in an across run and a down run, so it can only hold a number both allow. Where a 16 across in two squares (only 7 + 9) crosses a 23 down in three (only 6 + 8 + 9), the square must be 9, the one number both runs can use. A number every way needs. If every combination left for a run contains a 9, and only one of its squares can still take a 9, that is where it goes.
Kakuro combinations table
The cheat sheet every kakuro solver keeps nearby: give it a number of squares and a sum and it lists every set of different numbers from 1 to 9 that makes it.
How it was checked
The solver was run on all 110 puzzles of the daily kakuro. It found each one's stored answer, and found it to be the only one. Every step it explained was checked against those answers: it never placed a wrong number and never crossed off a right one, and 97 of the 110 were explained from the first square to the last without a guess.
More number puzzles
A new kakuro is waiting every day on the daily kakuro page. The sudoku solver handles killer sudoku, which uses the same sums, and the KenKen solver adds products and differences. For the same satisfaction in wood and metal, see our brain teasers. There are more solvers on the puzzle tools page.
Frequently Asked Questions
How do you solve a kakuro step by step?
Start with the runs that can only be made one way, like 3 in two squares (1 + 2) or 24 in three (7 + 8 + 9). Then cross the runs: each white square can only hold a number its across run and its down run both allow. When every way to fill a run needs a certain number and only one square can take it, it goes there.
What are the kakuro combinations?
The sets of different numbers from 1 to 9 that make each sum in a given number of squares. Some have only one: 16 in two squares is 7 + 9, 17 is 8 + 9, 6 in three is 1 + 2 + 3. The table on this page lists them all for any sum.
Can a number repeat in a kakuro run?
No. Within one run every number is different, though the same number can appear again in a different run in the same row or column.
What do the numbers in the black squares mean?
The number above the diagonal is the sum of the run of white squares to its right; the number below it is the sum of the run beneath it.
Does every kakuro have one solution?
A well-made one does. If the clues you enter allow more than one, the solver says so.