crowdsourcing: how far can we optimize this problem? Find a collection A of 5-element subsets of [1..21] such that every 4-element subsets of [1..21] is a subset of exactly one element of A
some pre-calculations: 21C5 = 20349 21C4 = 5985 21C4/5 = 1197 (A must have 1197 elements)
[serious]
Also, if we know that {1,2,3,4,5} in A, we know that other elements of A cannot intersect with {1,2,3,4,5} in 4 places, so we know that 80 5-element subsets are not in A
So, we need all subsets of length 4 starting with {1,2,4}. The first we don't have is {1,2,4,6}. We already have {1,2,6,7}. So {1,2,4,6,8} Is the first option