2

Part of 2000 Taiwan National Olympiad

Problems(1)

Connected intersections of k subsets

Source:

n

be a positive integer and

A=\{ 1,2,\ldots ,n\}

A

is said to be connected if it consists of one element or several consecutive elements. Determine the maximum

k

for which there exist

k

distinct subsets of

A

such that the intersection of any two of them is connected.

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