Kakuro Math Combinations Cheat Sheet
Every possible Kakuro combination for 2-cell through 5-cell runs. Print this page and keep it next to your puzzle book.
Kakuro combinations are the key to solving fast. Each sum-and-length pair limits which digits can fit a run. Memorize the short ones. Look up the long ones. This cheat sheet covers 2-cell through 5-cell runs.
2-cell runs (the easiest to memorize)
Sum 3: 1 + 2. Sum 4: 1 + 3. Sum 16: 7 + 9. Sum 17: 8 + 9. These four sums are unique. Only one pair of digits fits each.
Sum 5 through 15 each have two or more pairs. For example, sum 10 can be 1 + 9, 2 + 8, 3 + 7, or 4 + 6. You need cross-checks to narrow these down.
3-cell runs (worth memorizing the locked ones)
Sum 6: 1, 2, 3. Sum 7: 1, 2, 4. Sum 23: 6, 8, 9. Sum 24: 7, 8, 9. These are the locked kakuro combinations for 3 cells. Only one digit set fits.
Sum 8 through 22 each have two or more combos. Keep a cheat sheet for these.
4-cell runs
Sum 10: 1, 2, 3, 4. Sum 11: 1, 2, 3, 5. Sum 29: 5, 7, 8, 9. Sum 30: 6, 7, 8, 9. These are the locked 4-cell sets.
Most 4-cell sums have several combos. Use cross-checks across and down to lock in the digit order.
5-cell runs
Sum 15: 1, 2, 3, 4, 5. Sum 16: 1, 2, 3, 4, 6. Sum 34: 4, 6, 7, 8, 9. Sum 35: 5, 6, 7, 8, 9. These are locked.
Long runs feel hard but often have fewer combos. The math is tight. Less freedom for digits means faster solves.
How to use the cheat sheet
Print this page. Tape it inside the front cover of your kakuro book. When you start a run, glance at the sheet to see what is possible.
Over time, you will memorize the unique combos. The middle sums take longer to learn. Keep the sheet close.
Quick reference: digits that appear in every combo
For some sums, one or two digits show up in every possible set. Sum 11 in 4 cells always includes 1 and 2. Sum 30 in 4 cells always includes 9 and 8. Lock those in.
This is the fastest way to crack a tough kakuro grid. Find the locked digit. Place it. Move on.