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No two subsets of S with the same sum of elements

Source: Baltic Way 1998

January 11, 2011

combinatorics proposedcombinatorics

Problem Statement

Determine all positive integers

n

for which there exists a set

S

with the following properties: (i)

S

consists of

n

positive integers, all smaller than

2^{n-1}

; (ii) for any two distinct subsets

A

and

B

of

S

, the sum of the elements of

A

is different from the sum of the elements of

B

.

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