Cayley graph search with Claude Code: what puzzle competitions look like in 2026 (andlukyane.com)

Recent advancements in solving combinatorial puzzles using Cayley graphs have emerged from two Kaggle competitions within the CayleyPy series, focusing on the IHES Picture Cube and Megaminx puzzles. Participants utilized Claude Code, an AI tool, to automate various aspects of their workflows, allowing them to concentrate on strategic decisions rather than coding details. This shift in approach is significant as it illustrates the growing integration of large language models (LLMs) in research and development, enabling researchers to efficiently tackle complex search problems that were previously time-consuming and challenging. The competitions highlighted two crucial components: the application of learned distance heuristics combined with beam search algorithms to navigate the vast Cayley graphs representing puzzle states, and the agentic workflow enhancing productivity. A Cayley graph, which encapsulates the relationships between possible puzzle configurations through vertices and edges, is impractical for exhaustive searches due to its immense size. This necessitates a reliance on heuristics and intelligent search strategies. By leveraging Claude Code for automation—such as generating training scripts and optimizing search configurations—participants were able to explore innovative methods for reducing path lengths and improving competition scores, reflecting a deeper understanding of solving complex search problems in AI/ML.