MathDB

Six real numbers

x_1<x_2<x_3<x_4<x_5<x_6

are given. For each triplet of distinct numbers of those six Vitya calculated their sum. It turned out that the

20

sums are pairwise distinct; denote those sums by

s_1<s_2<s_3<\cdots<s_{19}<s_{20}.

It is known that

x_2+x_3+x_4=s_{11}

x_2+x_3+x_6=s_{15}

and

x_1+x_2+x_6=s_{m}

. Find all possible values of

m

Problem Statement