How To Solve Kakuro Puzzles
Fill in the blank squares with numbers from 1 to 9 so that the entered numbers add up to the sum required in the grey clue squares vertically and horizontally. The numbers in consecutive white cells that make up a sum must be unique (no duplicates).
Here is a typical Kakuro puzzle grid. The grid size can be smaller or larger and varies in difficulty.
Each white square contains an "across sum clue" and a "down sum clue." These clues can are found in the grey squares on the left or top of the run.
There can be no duplicate numbers in any consecutive white cells that make up a sum.
The solution to the puzzle is shown here.
Notice that the white cells, horizontally and vertically, add up to the corresponding sum in the grey square above and to the left. Further, there are no duplicate numbers in any consecutive white cells.
Some Common Strategies
Single Runs: Look for squares where the run is only one square long.
Lone Squares: A "lone square" is an empty square with all its neighboring squares (either column or row) filled in. Add the corresponding adjacent values and subtract the total from the clue. The remaining value is the answer for that square.
Cross Reference: Find two intersecting runs and compare the clue number combinations for each. Any values which appear in the combinations for both runs are candidates for the intersecting square. For example, if the down clue is 7 and only has one combination (1+2+4) and the across clue is 18 and has three possible combinations (3+7+8, 4+5+9, or 3+6+9), the only common number in both sets of combinations is 4, so the intersection square must be 4.