The grid explained
A Kakuro grid looks like a crossword. It has white cells and dark cells. The dark cells either block off sections or hold clue numbers. White cells are where you write your answers.
Each dark clue cell can hold two numbers. The number in the top-right corner is the clue for the white cells running to the right (the “across” clue). The number in the bottom-left corner is the clue for the white cells running downward (the “down” clue). Not every clue cell has both.
A group of consecutive white cells that share one clue is called a “run.” Every run has exactly one clue number. Your job is to fill each run with digits 1 through 9 so they add up to the clue.
The three rules of Kakuro
Rule 1: Digits 1 through 9 only
You can only use the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9. Zero is not allowed. Double-digit numbers are not allowed.
Rule 2: Match the sum
The digits in each run must add up to the clue number. If the clue says 10 and the run has three cells, you need three digits that add up to 10. For example: 1 + 3 + 6, or 2 + 3 + 5.
Rule 3: No repeats within a run
You cannot repeat a digit in the same run. If a three-cell run adds up to 6, you cannot use 2 + 2 + 2 because that repeats the 2. You must use 1 + 2 + 3.
Key number combinations to memorize
Some clue numbers only have one possible combination. These are the first cells you should fill in because they give you guaranteed information.
| Clue | Cells | Only combination |
|---|---|---|
| 3 | 2 | 1 + 2 |
| 4 | 2 | 1 + 3 |
| 16 | 2 | 7 + 9 |
| 17 | 2 | 8 + 9 |
| 6 | 3 | 1 + 2 + 3 |
| 7 | 3 | 1 + 2 + 4 |
| 23 | 3 | 6 + 8 + 9 |
| 24 | 3 | 7 + 8 + 9 |
| 10 | 4 | 1 + 2 + 3 + 4 |
| 11 | 4 | 1 + 2 + 3 + 5 |
| 29 | 4 | 5 + 7 + 8 + 9 |
| 30 | 4 | 6 + 7 + 8 + 9 |
| 15 | 5 | 1 + 2 + 3 + 4 + 5 |
| 35 | 5 | 5 + 6 + 7 + 8 + 9 |
| 45 | 9 | 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 |
Memorizing these combinations will speed up your solving by a lot. They are the backbone of every Kakuro strategy.
How to solve your first puzzle
- Look for unique combinations. Scan the grid for clues that have only one possible combination. A sum of 3 in two cells is always 1 and 2. Write in the pencil marks.
- Check where runs cross. When an across run and a down run share a cell, the digit in that cell must satisfy both clues. This narrows your options fast.
- Eliminate impossible digits. If a cell is part of a run where 7, 8, or 9 are not possible, cross those out. The fewer options left, the closer you are to the answer.
- Fill in forced cells. When a cell has only one possible digit remaining, write it in. Then go back and update the pencil marks in all connected runs.
- Repeat until solved. Each digit you place gives you more information about the cells around it. Keep cycling through the grid until every white cell is filled.
Tips for beginners
- Start with a small grid (4x4 or 6x6). Do not jump into a 12x12 on your first try.
- Use pencil marks. Write small candidate digits in each cell until you are sure.
- Keep a combinations cheat sheet nearby until you have the common ones memorized.
- If you are stuck, look for the longest and shortest runs. They often have the fewest options.
- Do not guess. Every Kakuro puzzle has one solution that you can find with logic alone.