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2014 China Second Round Olympiad Second Part Problem 3

Source: 2014 China Second Round Olympiad

August 4, 2015

Chinacombinatorics

Problem Statement

Let

S=\{1,2,3,\cdots,100\}

. Find the maximum value of integer

k

, such that there exist

k

different nonempty subsets of

S

satisfying the condition: for any two of the

k

subsets, if their intersection is nonemply, then the minimal element of their intersection is not equal to the maximal element of either of the two subsets.

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