Light Up: the only light
Every dark cell needs a bulb that can see it. When only one cell can still light it, the bulb goes there. When a bulb would leave something short, the cell is out.
How it works
A dark cell will be lit by a bulb somewhere in its row or column, or by a bulb in the cell itself. Cross off every cell that is dotted, lit or behind a black cell. If one candidate is left, the bulb goes there. This is elimination.
When that runs dry, test a cell. Suppose a bulb sits there. Its light closes every cell it reaches. If some number can no longer reach its count, or some dark cell has nothing left that can light it, the supposition led to a contradiction. The cell gets a dot.
That is proof by contradiction. You never place the test bulb; you only prove it can’t go there.
Which cells to test
Test cells that see a lot: a bulb there closes many cells at once. Test cells beside a number that has little room to spare, and cells in line with a dark cell that has only two possible lights.
The shape of the argument
Suppose a bulb in cell X. Then the 2 has one bulb and no open sides. But the 2 needs two bulbs. Both can’t be true, so the supposition is false: no bulb in X.
Worth memorizing
Every dark cell has a light somewhere in its row, its column or itself.
One candidate left: the bulb goes there.
A test bulb that leaves a number short or a cell dark is out.
Dot the cell. Never place the test bulb.
Practice
0 of 4 rightSuppose a bulb sat on the ringed cell. What goes wrong?
Which cell can still light the ringed cell?
The numbers are done. Which cell must light the ringed cell?
Suppose a bulb sat on the ringed cell. What goes wrong?