How to Solve Kakuro: Step-by-Step Tutorial
A hands-on walkthrough of solving a real Kakuro puzzle from the first cell to the last. Follow along at your own pace.
This is a hands-on tutorial. We will walk through a real Kakuro puzzle from start to finish. Grab a pencil and follow along.
Step 1: Read the grid
Look at the puzzle. White cells need digits. Dark cells with numbers are clues. A number in the top-right corner of a dark cell is the sum for the white cells running to the right. A number in the bottom-left is the sum for the white cells running downward. Identify all the runs (groups of connected white cells sharing a clue).
Step 2: Find unique combinations
Scan every clue for ones that have only one possible combination. A 2-cell run with a sum of 3 must be 1 and 2. A 2-cell run with a sum of 17 must be 8 and 9. A 3-cell run with a sum of 6 must be 1, 2, and 3. Write these candidates as small pencil marks in each cell. You know the digits. You just do not know the order yet.
Step 3: Cross-reference
Now look at cells where two runs cross. That cell must have a digit that appears in both the across candidates and the down candidates. If the across run candidates are 1 and 2, and the down run candidates are 2, 3, and 4, then the crossing cell must be 2. Write it in with confidence.
Step 4: Eliminate and propagate
Every digit you place changes the possibilities for its neighbors. When you place a 2 in a cell, go to every other cell in both runs and remove 2 from their pencil marks. Then recalculate the remaining sum. If a 3-cell run with a sum of 10 now has a 2 placed, the remaining two cells must sum to 8 without repeating the 2. That limits your options and often solves another cell.
Step 5: Repeat
Cycle through the grid: find forced cells, place digits, update pencil marks, cross-reference again. Each pass through the grid gives you more information. Easy puzzles take two or three passes. Hard puzzles take many more. If you feel stuck, focus on the runs with the fewest remaining candidates. They are the most likely to crack open.
Common beginner mistakes
Forgetting the no-repeat rule within a run is the most common mistake. Double-check that you never use the same digit twice in one run. Another mistake is forgetting to update pencil marks after placing a digit. Stale pencil marks lead to contradictions that are hard to trace back. Stay disciplined and the puzzle will fall into place.