Trial and Refutation
Try a cell both ways: reject a branch that fails, or keep any other mark both surviving branches agree on.
How it works
- 1Only two cells in the whole grid can light the top-right corner: the corner itself and the marked cell under it, because the 1's wall cuts the corner's row and another wall cuts its column two down.
- 2Nothing here follows by ordinary reasoning, so suppose a bulb goes in the cell directly below the 1, and follow it.
- 3It lights its own whole row, which empties the cell under the corner; and it fills the 1, which empties the 1's other neighbours — the corner among them.
- 4Both of the corner's sources are gone, so the supposition strands it in the dark forever: the cell below the 1 is empty. The same rung also tries EMPTY when that is the forcing branch, and keeps consequences shared by both branches. Needing any trial form is what makes a board Extreme.
- Cells that establish the pattern
- Cell this technique rules out