MathDB
Complete set of weights

Source: Iran second round- 2013- P2

May 4, 2013
inductioncombinatorics proposedcombinatorics

Problem Statement

Let nn be a natural number and suppose that w1,w2,…,wn w_1, w_2, \ldots , w_n are nn weights . We call the set of {w1,w2,…,wn}\{ w_1, w_2, \ldots , w_n\} to be a Perfect Set if we can achieve all of the 1,2,…,W1,2, \ldots, W weights with sums of w1,w2,…,wn w_1, w_2, \ldots , w_n, where W=∑i=1nwiW=\sum_{i=1}^n w_i . Prove that if we delete the maximum weight of a Perfect Set, the other weights make again a Perfect Set.
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