MathDB

3

Part of 2014 China Second Round Olympiad

Problems(1)

2014 China Second Round Olympiad Second Part Problem 3

Source: 2014 China Second Round Olympiad

8/4/2015
Let S={1,2,3,⋯ ,100}S=\{1,2,3,\cdots,100\}. Find the maximum value of integer kk, such that there exist kk different nonempty subsets of SS satisfying the condition: for any two of the kk 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.
Chinacombinatorics