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Cono Sur Olympiad 2013, Problem 1

Source:

August 22, 2014
algebra proposedalgebra

Problem Statement

Four distinct points are marked in a line. For each point, the sum of the distances from said point to the other three is calculated; getting in total 4 numbers.
Decide whether these 4 numbers can be, in some order: a) 29,29,35,3729,29,35,37 b) 28,29,35,3728,29,35,37 c) 28,34,34,3728,34,34,37
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