How the Vanishing Piece works

No alien leaves the picture. Each one hands a thin slice of itself to its neighbor, so nine slightly taller aliens fill the space of ten.

A straight cut across the stairs

The aliens stand on stairs, each one pixel higher than the last. The cut is a straight line, so it crosses each alien at a different height. It misses the first alien. It passes just under the antenna tips of the second, a little lower on the third, and under the feet of the last.

The swap

Swapping the top pieces moves every alien’s top part one place to the left. Now each bottom part wears the top part of its neighbor. Every new alien is whole, with one row of pixels shown twice: longer antennae on one, bigger eyes on another, longer legs on a third. The last step gets only sky.

Before (top) and after (bottom): the top part shifts one place left, and 5 aliens of 4 rows become 4 aliens of 5 rows. The boxed row in each is shown twice.

Where did it go?

The ten aliens had 90 rows of pixels between them, and the nine still do: the lost alien’s rows were shared out, one to each of the others. Each grows by one row out of nine, about a ninth taller. The change is spread so thin that nothing looks stretched, so your brain simply counts. Swap back and every slice goes home: ten again. Famous vanishing puzzles work the same way, like Sam Loyd’s Get Off the Earth from the 1890s and the Vanishing Leprechaun.