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set with conditions, |F|≠1996

Source: Yugoslav TST 1996 P1

May 16, 2021
Setsnumber theorysetcombinatoricscombinatorics unsolved

Problem Statement

Let F={A1,A2,…,An}\mathfrak F=\{A_1,A_2,\ldots,A_n\} be a collection of subsets of the set S={1,2,…,n}S=\{1,2,\ldots,n\} satisfying the following conditions:
(a) Any two distinct sets from F\mathfrak F have exactly one element in common; (b) each element of SS is contained in exactly kk of the sets in F\mathfrak F.
Can nn be equal to 19961996?
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