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# Quarter Partitioning

The following problem was first posed to me by a fellow grad student, Elyse Yeager, at the University of Illinois.

You are sitting in front of a table, both blindfolded and wearing heavy gloves. On the table are a large number of quarters (in other words more than 20), 20 of which are heads up. You can move around and flip quarters but cannot feel which side is which.  Separate the quarters into two piles so that with 100% certainty the number of heads in both is equal.

Comments: You do not know if the total number of quarters is even or odd. You must know with 100% certainty, so this is not a slick probabilistic argument.  This is not a trick problem (you are not standing the quarters on their sides, etc.).

Solution below the fold…

Pick 20 random quarters and put them in a pile. There are $n$ quarters which are heads up in this pile and $20-n$ in the other. Flip over all the quarters in the first pile. Now both piles have $20-n$ coins which are face up.

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This entry was posted on April 29, 2012 by in Recreational Math and tagged , .