Unique Sum Partition (Magic Block)

Some sums have exactly one set of distinct digits. Fill the digits in, or cross out everything that is not part of the set.

Level 1 Sum knowledge Technique 03

Why it works

Kakuro digits are 1 to 9 and never repeat inside a run, so the number of ways to make a sum is fixed by mathematics, not by the puzzle. A run of two cells that sums to 17 can only be 8 + 9.

Players call these Magic Blocks. Learning the small ones by heart, such as 3 and 4 in two cells and 16 and 17 in two cells, or 6 and 7 and 23 and 24 in three cells, speeds up every puzzle.

The mirror rule doubles what you remember: replace every digit d by 10 − d, and a sum s in n cells becomes 10n − s in n cells. So 4 in two cells is {1,3} and 16 in two cells is {7,9}.

How to spot it

1. Read the clue sum and count the cells of the run.
2. Ask whether only one set of different digits can make that sum.
3. If it can, place those digits where the crossing runs allow, and remove every other digit from the cells of the run.

Practice it

Open the app, choose a level that uses this technique, and ask the coach for the next step. Every hint links back to this guide.