Light Up: following a chain
When the simple rules run dry, suppose a bulb (or no bulb) and follow the moves it forces. If a rule breaks, the opposite is true.
How it works
The one-bulb test looks one move ahead. Some grids need more. You suppose something about a cell, then keep applying the basic rules: finished numbers, numbers with no spare sides and only lights.
Each forced move leads to the next. If the chain ends with a number that can’t reach its count, or a cell nothing can light, the supposition was false. This is a bulb chain, and it is still proof by contradiction.
You never write the chain on the grid. You only write the one conclusion it proves.
Where to start a chain
Test cells next to numbers that are almost decided, and cells that many dark cells depend on. A chain that runs through several numbers breaks quickly.
Try both ways. Supposing no bulb can break the grid just as supposing a bulb can.
Worth memorizing
Suppose, then follow only forced moves.
Never guess a second time inside the chain.
A broken rule proves the opposite.
A bulb if you supposed none, a dot if you supposed one.
Write only the conclusion.
Practice
0 of 2 rightFollow the forced moves from this supposed position. What happens?
Supposing no bulb on the ringed cell breaks a rule. What goes in it?