If $n^2+1$ people are lined up, there are $n+1$ whose heights are increasing or decreasing

Asked Oct 28 '15 at 05:11

Active Oct 28 '15 at 05:32

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Suppose $n^2 +1$ people are lined up shoulder to shoulder is a straight line. Then it is always possible to choose $n+1$ of the people to take one step forward so that going from left to right their heights are increasing (or decreasing).

I know my teacher wants us to use the pigeonhole principle on this and so you know its not a difficult proofs class, but please explain the calculus if your using summation as it's my hardest thing to grasp, my teacher forgets to show us the calculus or explain it sometimes.

edited Oct 28 '15 at 05:32

asked Oct 28 '15 at 05:11

hurl3y

See also http://math.stackexchange.com/a/316019 http://math.stackexchange.com/q/619088 http://math.stackexchange.com/q/587961 – Oct 28 '15 at 05:17
And also see this question for an explanation that $n^2+1$ is the minimum. – Jyrki Lahtonen Oct 28 '15 at 05:45

If $n^2+1$ people are lined up, there are $n+1$ whose heights are increasing or decreasing

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