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 $26$.
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 $26$.
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 $1000$.