Over the last couple of months, the author worked on two Kaggle competitions in the CayleyPy series: IHES Picture Cube and Megaminx. Both are combinatorial puzzle solvers reformulated as a search in an enormous implicit Cayley graph, where each puzzle state is a vertex, each possible move is an edge, and solving means finding a short path back to the identity. The author used Opus inside Claude Code as the implementation agent for both competitions. Claude wrote essentially all of the training scripts, beam-search variants, TPU ports, submission automation, and post-processing tools. The author still reviewed the code, checked outputs, and made the experiment-level decisions. The post covers two topics: working with Cayley graphs by combining learned distance heuristics, wide beam search, symmetry, and path post-processing to solve puzzle graphs too large for DFS/BFS; and the agentic workflow where the agent handles implementation and the human role shifts toward experimental design, plateau detection, and search strategy. The leaderboard shows a single number (total moves over a fixed set of scrambles), and score improvement indicates the ability to find shorter paths.