Can LLMs identify 16 cards in 45 bit-queries? (snwagh.com)

Recent research explores the capabilities of large language models (LLMs) in tackling a complex mathematical puzzle involving the identification of cards with limited queries. The challenge involves 16 uniquely encoded cards, each representing a 4-bit value, where the objective is to determine their arrangement using fewer than 50 binary queries about their properties (red or king). The current best-known strategies require at least 45 queries, aligning with theoretical limits derived from information theory, which assert that the definitive minimum cannot exceed 64 checks for this scenario. Significantly, the study not only highlights the emerging ability of LLMs to address open mathematical problems but also illustrates their potential in exploring optimal strategies through adaptive querying, akin to how they function in natural language processing. By employing an LLM agent to generate and evaluate strategies over numerous iterations, researchers were able to refine approaches towards achieving optimal query counts, illustrating a practical application of AI in mathematical exploration. This intersection of AI and combinatorial game theory opens avenues for further research and could enhance understanding in both fields, especially in complex problem-solving scenarios beyond mere computational brute force.