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Regional Olympiad - FBH 2011 Grade 10 Problem 4

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2011

September 26, 2018

combinatoricsSets

Problem Statement

Let

n

be a positive integer and set

S=\{n,n+1,n+2,...,5n\}

a)

If set

S

is divided into two disjoint sets , prove that there exist three numbers

x

y

and

z

(possibly equal) which belong to same subset of

S

and

x+y=z

b)

Does

a)

hold for set

S=\{n,n+1,n+2,...,5n-1\}