MathDB

A set of

n

distinct integer weights

w_1,w_2,\ldots, w_n

is said to be balanced if after removing any one of weights, the remaining

(n-1)

weights can be split into two subcollections (not necessarily with equal size)with equal sum.

a)

Prove that if there exist balanced sets of sizes

k,j

then also a balanced set of size

k+j-1

b)

Prove that for all odd

n\geq 7

there exist a balanced set of size

n

Problem Statement