Storming Kaggle Cayley puzzles 555 and 666 with Claude vs Codex

AndLukyane · x · 2026-08-23

The author tackled Kaggle Cayley puzzles 555 and 666 using Claude and Codex, and explains why they're harder:

Larger solution space and diameter hurt: models move toward solutions iteratively, so each extra step compounds error; longer paths make correct labels scarcer, and random walks get lost or fail to reach distant points.
The pipeline reuses earlier approaches: initial model training, then polishing and beam search; a transformer was dropped as too slow.
After several days of training on an A100, the resulting model doesn't solve every puzzle but performs consistently.

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