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Rosen-Pigeonhole Principle

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An arm wrestler is the champion for a period of 75 hours. (Here, by an hour, we mean a period starting from an exact hour, such as 1 P.M., until the next hour.) The arm wrestler had at least one match an hour, but no more than 125 total matches. Show that there is a period of consecutive hours during which the arm wrestler had exactly 24 matches.
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It is just a prove, no mathematics behind it

$1\leq a_{1}\leq a_{2}\leq .............\leq a_{75}\leq 125$

Now, say $b_{i}=a_{i}+24$

So, $25\leq b_{1}\leq b_{2}\leq .............\leq b_{75}\leq 149$

Now, in time interval between $\left [ 1...24 \right ]$ $a$ played all matches

So, in that time arm wresler played exactly 24 matches

http://www.cse.iitd.ernet.in/~naveen/courses/CSL105/solu5.pdf

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