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Some n distinct sums of the form x_p+x_q+x_r are zero

Source: Bulgarian MO 2003: P1

May 22, 2014
pigeonhole principlesymmetrycombinatorics unsolvedcombinatorics

Problem Statement

Let x1,x2…,x5x_1, x_2 \ldots , x_5 be real numbers. Find the least positive integer nn with the following property: if some nn distinct sums of the form xp+xq+xrx_p+x_q+x_r (with 1≤p<q<r≤51\le p<q<r\le 5) are equal to 00, then x1=x2=⋯=x5=0x_1=x_2=\cdots=x_5=0.
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