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Romania TST 2021 Day 2 P2

Source:

June 13, 2021

combinatoricsSetsromaniaRomanian TSTTST

Problem Statement

Consider the set

M=\{1,2,3,...,2020\}.

Find the smallest positive integer

k

such that for any subset

A

of

M

with

k

elements, there exist

3

distinct numbers

a,b,c

from

M

such that

a+b, b+c

and

c+a

are all in

A.

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