Stephen J. Pursey · Lakewood, Ohio
It takes eleven cubes to hide emptiness.
There are exactly 384 ways — counted, and explained, in 2026.
I hated math as a kid. Now I stay up late doing it for fun — answering questions nobody has answered, and asking questions nobody has asked.
minimal cavity polycube · 11 cells · drag to rotate · A396101(11) = 384
Latest
A cavity-aware enumeration algorithm
The methods paper: cavity-aware pruning with proven exactness, measured 13–20× over the direct approach, with sizes 19–20 as the demonstration. Design validated; computation scheduled.
The full ledgerBriefly
Greetings from Lakewood, Ohio, on the shore of Lake Erie, where I work as a supply-chain analyst by day. By night I am a hobbyist mathematician; my current obsession is the computational enumeration of polycubes, particularly those enclosing internal cavities (A357083, A355966, A396101 — the last one mine). Other interests include piano, self-hosted computing, and the collecting of precise, rare, and archaic English words.
All of this is a hobby. Amateur mathematics is a living tradition with room in it for you — the door was open the whole time.
The open questionsTry it yourself
Build your own eleven-cube
The amber cell in the middle wants out. Place cubes in the 3×3×3 frame until it has no face-path to the outside — and everything you placed hangs together as one piece. The minimum is 11. The theorem is that you can't do better; the game is finding one at all.
0 cubes placed · 11 is the minimum
And the question that started everything: how many distinct minimal builds exist? (Fixed in space — rotations count separately.)