Light Up (puzzle)

As of 2011, three books consisting entirely of Light Up puzzles have been published by Nikoli.

A typical starting point in the solution of a Light Up puzzle is to find a black cell with a 4, or a cell with a smaller number that is blocked on one or more sides (for example, a 3 against a wall or a 2 in a corner) and therefore has only one configuration of surrounding bulbs.

For example, a light bulb placed diagonally adjacent to a 3 will block two of its surrounding cells, making it impossible to have three bulbs around it; therefore, the diagonal cells around a 3 can never have lights in them and can be always dotted.

Similarly, one may put dots in places where a bulb would "trap" another unlit cell, making it impossible to light it up without breaking the rules.

For example, there may be a long area on a border, with multiple black squares one space away.

Another common deduction involves a rectangle, with none of the four corners next to a numbered black square.

[1] This is proved by a polynomial-time reduction from Circuit-SAT, which is known to be NP-complete, to Light Up puzzles.