Cayley graph search with Claude Code: what puzzle competitions look like in 2026

Cayley graph search with Claude Code: what puzzle competitions look like in 2026 Over the last couple of months I worked on two Kaggle competitions in the CayleyPy series: IHES Picture Cube and Megaminx. Both are combinatorial puzzle solvers, and they can be reformulated as a search in an enormous implicit Cayley graph: each puzzle state is a vertex, each possible move is an edge, and solving means finding a short path back to the identity. This is a long term activity: we were researching these puzzles for a couple of years and published several papers. This year we took another step to solving them. I remember working on this in 2024. At that time, all code was written by hand, and I spent a lot of time on debugging it and digging into documentation. But much changed in these two years: nowadays, agentic workflows are a significant part of my workflow and I can delegate a lot of the implementation work to an LLM, focusing on decisions and not on specifics (even though I have to…