Minimum and Maximum Sum Bounds

The remaining sum of a run bounds what each of its cells can hold. Digits outside the bounds can be removed.

Level 2 Sum knowledge Technique 06

Why it works

A cell can be no smaller than the remaining sum minus the largest digits the other cells could take, and no larger than the remaining sum minus the smallest digits the others need.

A simple form: in a run that still needs 17 across two cells, no cell can be smaller than 17 − 9 = 8, so only 8 and 9 remain. Bound reasoning turns a wide candidate list into a short one without placing anything.

How to spot it

1. Find the remaining sum of the run.
2. For each empty cell, subtract the largest possible total of the other cells from the remaining sum to get a lower bound.
3. Subtract the smallest possible total of the other cells to get an upper bound.
4. Remove every candidate outside the bounds.

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.