Lab record 03 · Hamiltonian cycle

Snake

The counterpoint to the 2048 solver. 2048 has random spawns, so no strategy can promise a win. Snake is deterministic — and this AI carries an actual proof: it never dies, and it fills all 144 cells, every time. Turn on the cycle overlay to see why.

Snake Apple Cycle

↑ ↓ ← → or WASD to steer · Space AI · C cycle · R new game Swipe the board to steer

Apples 0

Best 0

Length 3

Steps 0

Policy telemetry

Last decision: —
Cells skipped: —
Cycle position: —
Cycle steps to apple: —
Board filled: 2%

Read tail → head, the cycle indices always increase. Every body cell therefore sits at or below the head’s index, so any neighbour with a higher index cannot be the body — and moving there keeps the property true. The next cell along the cycle always qualifies, so a legal move always exists.

Policy

Shortcuts

Strict cycle walks the loop and nothing else — the slowest, most obviously correct version. Guarded takes the largest jump the invariant allows, finishing in roughly a third fewer steps with the same guarantee.