Ever since Christmas 2024, when I was still preparing for the NOI Provincial Team Selection Competition (which I would later fail), I had already completed the game Shapez1 and built a working Everything Machine. Well, accurately speaking, not every shape can be made from it. It’s designed for random 4-layer full shapes, the kind you get in freeplay2 (so e.g., rocket shape is excluded). Since then, I’ve been fixated on making a genuine Everything Machine that supports any layer count and fills in the void spaces inside shapes. So the first thing I needed to do was figure out which shapes could actually be built using stackers, rotators, and cutters. I even had a dream back then: if I could fully solve the reachability problem (preferably with an efficient algorithm), I could turn it into an OI problem.

After going through a series of random attempts, I put this project on hold for over a year. Now, it’s time to finish what we started but left unfinished before.

  1. Shapez Demo https://shapez.io/
    Steam Webpage https://store.steampowered.com/app/1318690/Shapez/ ↩︎

  2. Freeplay refers to levels 27 and above. All levels before this have a specific shape requirement. From level 27 onward the shape requirements are randomly generated shapes starting with 2 layers and going up to 4 layers at the most. ↩︎