Choose any $38$ different natural numbers less than $1000$.

Prove that among the selected numbers there exists at least two whose difference is at most $26$.

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    $\begingroup$ I don't think this question has much to do with probability or statistics, but see, for example, this question to get an idea on how this one can be approached. Maybe you should edit the tags accordingly. $\endgroup$ – Dilip Sarwate Mar 9 '12 at 16:09

Arrange the numbers in increasing order. The smallest number is $\ge 1$. If all differences between consecutive numbers are $27$ or more, then the biggest number is $\ge 1+ (27)(37)$, which is $1000$.


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