Kakuro: play free cross sums puzzles online

What is kakuro?

Kakuro is a number puzzle laid out like a crossword. Instead of words, you write digits from 1 to 9, and instead of written clues, each line of white cells has a sum. The cells in that line, called a run, must add up to it, and a digit may not repeat inside the run. That is the whole rulebook, yet the puzzles range from relaxing to properly tough.

The puzzle is also known as cross sums. It first appeared in American puzzle magazines under that name and became a hit in Japan, where the publisher Nikoli shortened the Japanese name to kakuro. It spread across British newspapers soon after sudoku did, and the two often share a page today.

How to play kakuro online here

Tap a white cell, then tap a number on the pad. On a computer you can use the arrow keys to move, type 1 to 9 to fill a cell, and press Backspace to clear it. The two runs through the selected cell light up, and their clues are marked in gold, so you always know which sums you are working with.

A few tools help when you get stuck:

• Notes turns taps into pencil marks, so you can keep track of the candidates in a cell. The N key does the same.
• Combos shows every combination of digits that still fits the selected runs, based on what you have already placed.
• Hint fills in one cell for you.
• A wrong digit shakes and turns red, and counts as a mistake. You can erase it and try again.

Pick Easy (6×6), Medium (8×8) or Hard (10×10) on the start screen. Each puzzle is checked by a solver before you see it, so there is always exactly one answer.

Kakuro combinations cheat sheet

Strong kakuro players know the sums that can only be made one way. When you spot one of these clues, you already know which digits belong in the run, and only their order is left to work out.

There is a pattern behind the table. The smallest sum of a run uses the lowest digits, and the next one up swaps only the largest of them. The same works from the top: the biggest sum uses the highest digits, and one less swaps the smallest of those. So once you remember that 3 cells can add up to 6 at the least and 24 at the most, the clues 7 and 23 follow on their own.

A simple way to solve a kakuro

1. Scan for the unique sums from the table and write their digits in as notes.
2. Where one of those runs crosses another, keep only the digits both runs allow. A cell in a run of 1 + 2 that crosses a run needing 2 or 4 must be 2.
3. Look at short runs with a big or small sum. Two cells adding up to 15 can only use 6 to 9, which rules out many digits in the crossing runs.
4. When a run has one cell left, subtract the digits already placed from its clue. That gives the last digit at once.
5. Keep going around the grid. Each digit you place makes the next one easier.

Kakuro, sudoku and killer sudoku

Kakuro shares the no-repeat rule with sudoku, but there are no rows of nine to complete and no boxes. The sums carry all the information. If you like the arithmetic, killer sudoku combines both ideas: sudoku rules plus cages that add up to a total, and it uses the same combination tricks. For a puzzle with all four operations, try Calcudoku. If you want plain logic without numbers to add, sudoku and Futoshiki are good next stops.

How to play Kakuro

1. Fill every white cell with a digit from 1 to 9.
2. A run is a line of white cells across or down. Its clue sits in the dark cell just before it: the number above the diagonal is the across sum, the number below it is the down sum.
3. The digits in a run must add up to its clue.
4. A digit can appear only once in each run.
5. Every puzzle has exactly one solution.

Kakuro tips

Start with the runs that have only one answer

Some sums can only be made one way. Two cells that add up to 3 must be 1 and 2. Two cells that add up to 17 must be 8 and 9. Look for these first, then use the crossing runs to decide which digit goes where.

Cross the two runs through a cell

Every white cell belongs to an across run and a down run. A digit is only possible if both runs allow it. If the across run needs 1 or 2 and the down run needs 2 or 4, the cell is 2.

Use notes for the hard cells

Turn on Notes and tap digits to pencil in the candidates of a cell. When a cell narrows down to one digit, turn Notes off and place it. Combos lists every combination that still fits the selected runs.

Mind the edges of the range

Big sums in short runs need big digits, and small sums need small ones. Four cells adding up to 30 can only use digits from 6 to 9, so a 1 or 2 never fits there.

Frequently asked questions