Question 5
Two permutations $(a_1,\ldots,a_{2010})$ and $(b_1,\ldots,b_{2010})$ of $1,\ldots,2010$ intersect if $a_k=b_k$ for some $k$. Prove that there exist 1006 permutations such that every other permutation intersects at least one of them.
Proposed by Gregory Galperin (credit in the supplied notes).
Proposed by Gregory Galperin (credit in the supplied notes).