How to Solve Kakuro Puzzles

Overview:

The numbers in the gray squares are sums. The goal is to fill in the empty white squares with single digits that add up to the sum displayed to the left or above a block of squares. Numbers can appear only once in any block. Thus, for example, a 2-block answer to the sum of 4 can never be 2,2.

Start with the short blocks first, preferably two intersecting 2-square blocks with high number sum clues. Look for common numbers, which are easier to find with intersecting high sum clues. As with Sudoku, pencil in possible answers and look for numbers that are the only possibility for a square.

Example:

Step 1: Look for sums with only 2 possible answers (e.g., 16).

Step 2: Because duplicates are not allowed, 7 cannot be an answer for the sum of 14. 

Step 3: 9 must be the answer for the sum of 14, so 7 must be the other answer for the sum of 16.

Step 4: So 5 must be the other answer for the sum of 14.

Step 5: 5 must be an answer for the sum of 8,  so the other answers must be 2 and 1. But the answers for 15 must be 7, 2, 6.

Step 6: Then the full answer for 8 must be 5, 2, 1.

Step 7: Since 1 is also an answer for the vertical 8, the possibilities for the other 2 squares are 2, 3, 4, or 5.

Step 8: There are no zeros in kakuro, so 5 cannot be an answer for the sum of 5.

Step 9: The possible counterparts in the other square for 5 would then be 3, 2, or 1.

Step 10: Only single digits are allowed so 1 and 2 will not work for 12.

Step 11: So the other space for 12 must be 9 and the other space for 5 must be 2. 

Step 12: 20-9-6=5 and 8-1-2=5.

Love puzzles? Browse our puzzle books in the Books section. In particular, check out the Elusive Kakuro Puzzle Book.