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a partition in three non-empty subsets...

Source: Third Zhautykov Olympiad, Kazakhstan, 2007

April 25, 2007
inductioncombinatorics proposedcombinatorics

Problem Statement

The set of positive nonzero real numbers are partitioned into three mutually disjoint non-empty subsets (A∪B∪C)(A\cup B\cup C). a) show that there exists a triangle of side-lengths a,b,ca,b,c, such that a∈A,b∈B,c∈Ca\in A, b\in B, c\in C. b) does it always happen that there exists a right triangle with the above property ?
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