Kakuro Revisited

How to solve Kakuro

A Kakuro puzzle is a grid of white cells and black clue cells. Each clue belongs to a run: a line of white cells going right (an Across run) or down (a Down run). The run must add up to the clue, using digits 1 to 9, with no digit repeated.

1. Read the clues

A clue cell shows two numbers, split by a diagonal. The number in the top right is the sum of the run to the right. The number in the bottom left is the sum of the run below. Some cells show only one number, because there is only one run.

2. Find a run with one empty cell

This is the easiest step in Kakuro and it is often enough to start. If a run sums to 10 and already holds a 9, the last cell is 1. Nothing else fits, because digits cannot repeat and the sum is fixed.

3. Learn the small forced sums

Some sums have exactly one possible set of digits. In two cells, 3 must be 1 + 2 and 17 must be 8 + 9. In three cells, 6 must be 1 + 2 + 3 and 24 must be 7 + 8 + 9. These are called Magic Blocks, and knowing four or five of them by heart turns a slow start into a fast one.

Use the Sum Combinations Cheat Sheet to look up any sum and run length.

4. Cross the runs

Every white cell belongs to two runs at once. Work out which digits each run can still hold, then take the digits that appear in both lists. Often only one digit survives, and the cell is solved.

5. Keep pencil marks

Write the digits a cell can still hold in its corner, in small writing. The app does this for you: the individual digits in a cell are pencil marks, and the big digit is a placed answer. Keep the marks honest: when a digit is placed in a run, cross it out of the other cells of that run.

6. Never guess

Every Kakuro that this site publishes has one solution and can be solved by logic alone. If you are stuck, there is a technique you have not used yet. Open the coach in the app and it will walk you to the next step in four stages: where to look, the pattern, the logic and the conclusion.

A worked start

Take the board below. The across run of two cells on row 4 sums to 17. Two different digits that add to 17 can only be 8 and 9, so both cells hold one of those two digits. Nothing else can go there, and any other candidate in those cells is wrong.

Look for a clue that is a Magic Block on your next puzzle. Place those digits, then look for a run that is now one cell short. The puzzle unrolls from there.

Where to go next