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Esse Quam Videri

Is there a challenging math problem you really enjoyed solving?

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Possibly from SM Challenging Word Problems, or an old AMC test? There are a few that I enjoyed so much and recall distinctly-- anyone else remember solving Cheryl's birthday?-- and I was wondering if anyone has a fun one they'd like to share. It doesn't have to be the most difficult, just one you enjoyed. 

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A reader opens a book.  The sum of the left hand page number and the right hand page number is 313.  What are the page numbers?

This one is fun bc its gets the dc laughing as they consider possibilities. 

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I’ve seen a few variations on this one, but still remember running across it for the first time in middle school:

A group of students are pulling a prank. The school has exactly 100 students and 100 lockers. The first student enters and opens every locker. The second student enters, and closes every second locker starting with locker number two. The third student enters and closes or opens (closing the open ones and opening the closed ones) every third locker starting with number three. The fourth student enters and closes or opens every fourth locker starting with number four. This continues until the 100th student opens or closes the 100th locker. Which lockers are closed at the end?

One of the reasons it sticks with me is a comment from a math instructor that seemed rather inane, but it’s still a fun problem.

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