Given a set of size $25$, what is the minimum number of subsets of size $5$ such that all subsets of size $3$ are encompassed?
2026-03-25 10:59:44.1774436384
Combinatorial optimization - blocks & subsets
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Each 5-subset covers at most $\binom{5}{3}=10$ 3-subsets, so you need at least $\binom{25}{3}/10=2300/10=230$ 5-subsets. Bounds $[240,256]$ are given in the La Jolla Covering Repository.