Problem of the Week 1225
Square Peg in Square Hole
What is the side-length of the largest cube that can fit through a square hole drilled through a unit cube?
Precisely: We seek a hole in the cube (turning it into a topological torus) so that the new cube can fit through this hole.
Source: A Mathematical Space Odyssey, a very nice new book by Claudi Alsina and Roger Nelsen, published by the MAA. This problem has a long and interesting history, going back to about 1693.