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Not all are equal (Posted on 2011-12-03) Difficulty: 3 of 5
Given n distinct positive numbers a1,a2,...,an.
We construct all the possible sums (from 1 to n terms).

Prove that among those 2^n-1 sums there are at least n(n+1)/2 different ones.

Source: a problem from Soviet Union 1963 contest

No Solution Yet Submitted by Ady TZIDON    
Rating: 5.0000 (2 votes)

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Hints/Tips re: Solution ok, please edit | Comment 5 of 8 |
(In reply to Solution by John Dounis)

Nicely presented full-proof solution.

However - there is a minor typo: please edit:

"....Having costructing that then we can continue with the next set with size n-1:
                            s/b n-2.


  Posted by Ady TZIDON on 2011-12-07 22:57:20
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