We still haven't proven whether it's possible to always tile a rectangle perfectly using only squares of different, non-repeating sizes.
open
Mathematics & Logic
While specific solutions exist for certain rectangles, a full general theory predicting exactly which rectangles allow this kind of tiling remains incomplete. This puzzle blends recreational mathematics with serious combinatorics.
Team Humans Club. (2026). Problem WS01257: We still haven't proven whether it's possible to always tile a rectangle perfectly using only squares of different, non-repeating sizes.. World Solve. Retrieved 20 Jul 2026, from https://worldsolve.org/index.php?id=1257