This is a really well put together game. Before I started, I was a little overwhelmed by the description but as soon as I was in, the game was incredibly intuitive. I think for the Jam this is really great entry and fits the theme perfectly.
This game has some of the best balance between providing opportunity for the player to be clever and rewarding them for that. Constantly in the game the game I was always trying to think a head a keep track of where the faces were. And over the course of the game building up like a library of patterns such as knowing that 20 was just 6-4-6-4 back and fourth. Even the difficulty was well tuned taking me a couple goes on the final boss. I'd be interested in how you would take this further if were to add more bosses, perhaps a variety of floor tiles.
My only knit pick is in the UI, it's a small thing but keeping track of which bosses I have killed and when I do get a kill on a boss it can sometime be a bit jarring like "oh I did it" because I'm so focused on the left side. Anyway, great work.