MathDB

Let

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

, where

n\geq 3

. A subset

S

U

is said to be split by an arrangement of the elements of

U

if an element not in

S

occurs in the arrangement somewhere between two elements of

S

. For example, 13542 splits

\{1,2,3\}

but not

\{3,4,5\}

. Prove that for any

n-2

subsets of

U

, each containing at least 2 and at most

n-1

elements, there is an arrangement of the elements of

U

which splits all of them.

Problem Statement