How to Solve Kakuro: The Rules, the Shortcuts, and Your First Grid

If you can add to 45, you can solve kakuro. It looks like a crossword that lost its words, and that's close to what it is: a grid of white squares and shaded clue squares, where every run of white squares has to add up to the number at its start.

The format is slower and quieter than sudoku, and that's the point. One grid fills the gap between the gate and wheels up, or the hour after dinner when the group is still arguing about tomorrow's tee times.

The two rules

Every white square takes a digit from 1 to 9. Then:

1. Each run adds up to its clue. A clue on the left of a run is the target for the squares to its right. A clue on top of a column is the target for the squares below it.
2. No digit repeats inside a run. A two-square run that adds to 10 can be 1 and 9, 2 and 8, 3 and 7, or 4 and 6. It can never be 5 and 5.

That's everything. There's no third rule, no hidden scoring, and no guessing: a well-made kakuro has exactly one solution, and logic gets you all the way there.

The sums that only work one way

Most clues have several possible combinations. A handful have exactly one, and those are where every grid cracks open. Learn these and you'll recognize them on sight:

The pattern is easy to rebuild if you forget it. The smallest possible sum for a run uses the smallest digits, and the next one up only has one way to get there. The same holds from the top end down.

Your first grid

Here's a small one: two rows of three squares, three columns of two squares. The arrows show which way each clue reads.

Step 1: find the one-way sums. The top row is three squares adding to 6, and the table above says that can only be 1, 2 and 3. The bottom row is three squares adding to 24, which can only be 7, 8 and 9. You don't know the order yet, but you know the sets.

Step 2: work the crossings. Every column takes one digit from the top row (1, 2 or 3) and one from the bottom row (7, 8 or 9).

• The first column needs 12. From those two sets, only 3 + 9 makes 12. So A = 3 and D = 9.
• The second column needs 8. Only 1 + 7 works. So B = 1 and E = 7.
• That leaves 2 and 8 for the last column, and 2 + 8 = 10, which matches its clue. So C = 2 and F = 8.

Step 3: check every run. Top row: 3 + 1 + 2 = 6. Bottom row: 9 + 7 + 8 = 24. Columns: 12, 8 and 10. No repeats anywhere. Solved.

A full-size grid is the same three steps, repeated. Start with a one-way sum, find a square where it crosses another run, and use the second run to narrow the first.

Habits that save a grid

• Pencil, not pen. Write candidate digits small in the corner of a square, then erase as the crossings rule them out.
• Cross out the impossible. In a two-square run that adds to 10, a 5 can't appear, because it would need a second 5. In a two-square run that adds to 15, only 6, 7, 8 and 9 can appear.
• Use the leftovers. Once a run has all but one square filled, the last square is the clue minus everything else. It's the fastest move in the game.
• Check both directions. Every white square belongs to one across run and one down run. A digit that fits one and breaks the other is wrong.

Where to go from here

The jump from a six-square grid to a full page is mostly about volume: more runs, more crossings, more places to start. A book that starts small and grows with you makes that jump easier than diving into an expert grid.

That's what we built Kakuro for Beginners to do. It opens with a step-by-step tutorial and worked examples, then runs 100 puzzles that move from very easy to moderate, with full solutions at the back. When those feel easy, the Golf Course Kakuro volumes pick up where it leaves off.