IMO Shortlist 2013 problem A2


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Sept. 21, 2014
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Prove that in any set of 2000 distinct real numbers there exist two pairs a > b and c > d with a \neq c or b \neq d such that 
\left| \frac{a-b}{c-d} - 1 \right| < \frac{1}{100000} \text{.}
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