MathDB
F 11

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May 25, 2007
rational numbers

Problem Statement

Let S={x0,x1,⋯ ,xn}⊂[0,1]S=\{x_0, x_1, \cdots, x_n\} \subset [0,1] be a finite set of real numbers with x0=0x_{0}=0 and x1=1x_{1}=1, such that every distance between pairs of elements occurs at least twice, except for the distance 11. Prove that all of the xix_i are rational.
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