No islands
Every piece must keep a way to grow until it reaches the pump.
Count the free arms of two neighbouring pieces: the arms that do not lead anywhere yet. If joining the pieces would use up the last free arms of both, the joined piece would be an island, cut off from the rest. So that joint stays shut. Two lamps side by side are the smallest case.
How it works
Look at the pieces already joined and at their free arms.
Your turn
Four positions, each needing this lesson’s technique. The pinned tiles are given; turn the free ones until every lamp is lit. Click a tile to turn it, Ctrl+click to turn it back; right click or long press pins it.
Turn the free tiles so that every lamp lights up.
Why it works
Together with “no loops” this is the main tool in the middle of the board, where the edges no longer help. It also makes a group with only one way out take that way.