Locked Sum Residual

When a group of cells is locked to a fixed set of digits, its sum is fixed, and the rest of the run follows by subtraction.

Level 4 Combining runs Technique 11

Why it works

Suppose three cells of a run can only hold 2, 8 and 9 between them. Their total is 19, no matter which cell gets which. If the run needs 20, the remaining cell must be 1.

The same idea works across runs: two runs that share almost all their empty cells, with one extra cell, differ by exactly that extra cell.

How to spot it

1. Look for a set of empty cells in a run whose combined candidates are exactly as many digits as there are cells.
2. Add those digits: the sum is locked.
3. Subtract the locked sum from the remaining sum of the run to get the other cell.
4. Across runs, compare two runs with the same shared cells and one extra cell; the difference is that cell.

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.