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5 subsets with some propriety...

Source: Danube Mathematical Competition,Juniors #2

October 31, 2015

combinatoricsnumber theoryabsolute value

Problem Statement

Consider the set

A=\{1,2,...,120\}

and

M

a subset of

A

such that

|M|=30

.Prove that there are

5

different subsets of

M

,each of them having two elements,such that the absolute value of the difference of the elements of each subset is the same.