Chapter 6 - Section 6.2 - The Pigeonhole Principle - Exercises - Page 406: 22

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There are 101 people of different heights standing in a line, Note that $ 101=10^2 +1$. By Ramsey Theory, Every sequence of $n^2 + 1 $distinct real numbers contains a subsequence of length n + 1 that is either strictly increasing or strictly decreasing. Here n=10. So, it is possible to find 11 ( n+1) people in the order they are standing in the line with heights that are either increasing or decreasing.