MathDB
There exist 16 subsets of M

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October 15, 2010
linear algebramatrixcombinatorics proposedcombinatorics

Problem Statement

Let M={1,2,3,…,10000}.M=\{1,2,3,\ldots, 10000\}. Prove that there are 1616 subsets of MM such that for every a∈M,a \in M, there exist 88 of those subsets that intersection of the sets is exactly {a}.\{a\}.
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