MathDB

For every nonempty set

M{}

of integers denote

S(M)

the sum of all its elements. Let

A=\{a_1,a_2,\ldots,a_{11}\}

be a set of positive integers with the properties: 1)

a_1<a_2<\ldots<a_{11};

2) for every positive integer

n\leq 1500

there is a subset

M{}

A{}

for which

S(M)=n.

Find the smallest possible value of

a_{10}.

Problem Statement