A timeless geometric challenge by Sam Loyd…
The Mitre Puzzle is a classic dissection problem that asks: how can you cut a bishop’s mitre-shaped figure—a square with a triangular notch—into pieces that rearrange perfectly into a square?
Sam Loyd thought he had the answer with a four-piece solution. But there was a catch—his pieces actually formed a rectangle that just looked like a square. The illusion fooled many, but the puzzle wasn’t truly solved.
Enter Henry Dudeney, Loyd’s contemporary and fellow puzzle master. Dudeney showed a correct solution requiring five pieces, and for over a century, that was accepted as the minimal number needed.
Fast forward to 2024. Finnish mathematician Vesa Simonen shook things up by discovering several true four-piece solutions—finally cracking what was long considered impossible.

It’s interesting how even the oldest puzzles can still surprise us when we look closer.
You can explore Vesa Timonen’s innovative four-piece solution to the “Mitre Puzzle” on his dedicated webpage.
If you want to dive into Sam Loyd’s original puzzles, you can grab his classic book here.