Clue Exhaustion
Intermediate technique
Clue exhaustion is a simple but powerful rule: if the number of filled cells you've already placed in a line equals the total required by the clue sequence, then every remaining unknown cell must be empty.
The rule
For a line with clue a b c …, the total number of filled cells required is a + b + c + …. Count the filled cells currently in the line. If that count equals the clue sum, mark all remaining unknowns as empty.
Example
Line of length 10, clue 2 4 1. Clue sum = 7. You've confirmed 7 filled cells scattered across the line. The 3 remaining unknown cells must all be empty.
Why this is powerful
Clue exhaustion doesn't require the filled cells to be in their final grouped positions — it only requires the count to match. This means it fires even when runs are partially determined and separated by unknowns.
The technique is especially common in the later stages of a puzzle when constraint propagation has filled most cells. A single cross-line deduction can tip a row from "6 of 7 cells placed" to "7 of 7" — triggering exhaustion and clearing the rest of the row in one step.
Checking after every step
Because it's a cheap operation (just count), check for clue exhaustion after every deduction across any line. Solvers apply it automatically; humans can make it a habit to run a quick count on any line where they just placed a cell.
Related techniques
- Block capping — often precedes exhaustion
- Simple overlap — fills the cells counted here
- Contradiction method — for when exhaustion isn't enough