Techniques › 9 of 9
Line Contradiction (Bifurcation)
Level 5: Extreme
Assume a cell, follow every forced consequence, and if a line has no valid arrangement the opposite must be true.
Assume the highlighted cell in the bottom row is crossed out. That forces another cell, which forces another, and after a few steps column 1 cannot fit its clue.
An assumption that leads to a broken line is false, so the cell must be filled. In the app, the Why? tool shows exactly this chain for any empty cell.
This is the hardest technique here, but it never needs a guess: every step is forced.