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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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re(3): Solution Comment 8 of 8 |
(In reply to re(2): Solution by Ady TZIDON)

Ady,

It's sometimes more difficult to prove something that seems absolutely obvious than something that looks a bit more tricky.

Even so, in this case you are quite right. I even had the components (a,b,c,d,e,f,g) written out under my original solution. It was just a matter of reading them in the correct order and not getting distracted by irrelevancies.


  Posted by broll on 2011-12-08 13:52:12
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