Last night I stumbled upon a video showing a puzzle where just rotating the four pieces allowed for a fifth piece to be added. Figuring it had to be a trick, I grabbed a still frame and imported it into the Glowforge app, then traced over it with two lines and a square. I made the cuts and… It’s real?
So I did a little digging. It’s called Matsuyama’s Paradox. I went back into the app, figured out the size I needed for the fifth piece, did a little additional design work and here’s the result:
Both are made with identical cuts, but the numbered corners are orientated 180 degrees out.
Here’s the file if you want to play (Thanks for the tip, @lightner )