Contradiction
Extreme
Used by Smart Hint
When nothing else advances the puzzle, try one edge's two possible states and follow the consequences a few steps ahead. If one choice breaks a clue or a dot's rule, drives a line into a dead end, or finishes the board as anything but one single loop, the other choice is forced.
- Cells that establish the pattern
How it works
- When every other technique is stuck, pick any undecided edge and try one of its two possible states.
- Follow the consequences forward a few steps — the same techniques above, applied to what that one choice forces next.
- If within a handful of steps some clue ends up impossible to satisfy, or some dot ends up with too many lines, that choice can't be right.
- The edge is forced to the OTHER state instead — no different, in spirit, from a person saying "if this were a line, that corner over there couldn't work out — so it isn't." The search only ever looks a few steps ahead, matching what a person could actually trace by hand.