Parity: Fifteen

Thirty-six 15-puzzles form one 24 × 24 wall, every one of them a single swap from solved: 15 and 14 sit in each other's place. The tiles slide like gears in a diagonal wave, and when four marks line up on a diagonal the run lights up; a run that touches the stray pair fires a comet across the wall. Once a loop every puzzle comes home together, the pairs flip to try the swap, and parity turns them back. Half of all positions can never be solved.