Can an LLM solve this combinatorics problem?

Sixteen cards, four binary properties, and an LLM agent left alone with a machine and its weekends -- chasing D(16), the fewest probes that always pin down a hidden arrangement. It walked the best-known strategy down 64 → 60 → 49 → 47 → 46, one probe above the information floor, where an old ghost from sorting is waiting.