An old chestnut goes like this:

Three men check in to a hotel for one night, and pay $30 for it, up front, split evenly among themselves. Later, the owner realizes that the room really goes for $25, and being an honest man, sends the bellhop up to their room with the $5 change.

However, the bellhop decides the men are going to have trouble splitting the $5 three ways, and decides to pocket $2 himself and gives the men $3 which splits nicely.

So now the men have each paid $9, and the bellhop has $2 in his pocket for a total of $29. Where did the missing dollar go?

Answer

Unlike most of the old chestnuts, which I only consider so because I have seen them numerous times in different places, for this one I have a citation.

In The Math Chat Book by Frank Morgan (ISBN 0883855305), he writes that when he posed this puzzle on his web site, one reader wrote him to say that her father had posed this puzzle to her before World War II. Perhaps that explains the price.

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