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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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    I don't think this question has much to do with probability or statistics, but see, for example, [this question](http://math.stackexchange.com/q/91635/15941) to get an idea on how this one can be approached. Maybe you should edit the tags accordingly.2012-03-09

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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 $1000$.