Light Up: counting around numbers

A number on a black cell says exactly how many bulbs touch its four sides. Some sides are closed: the edge of the grid, another black cell, a dot, or a cell that is already lit. A lit cell is closed because a bulb there would shine on the bulb that lights it.

So each number is a small counting problem. Let need be the number minus the bulbs already beside it, and open the sides still free. If need equals open, every open side has a bulb. If need is 0, every open side has none.

This is elimination run both ways. The number rules out every arrangement with too few bulbs or too many, and when only one arrangement is left you can write it down.

A 3 with four open sides never has a bulb on a diagonal cell beside it. A bulb there would light two of the 3’s sides at once, leaving only two open sides for three bulbs. Dot the four diagonal cells. The same test works on a 2 with exactly three open sides.