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a riddle

On a nice day in the 1940’s, three girls go into a hotel and ask for a triple. The manager says sorry, no triples are available, so he puts them in three singles, at $10 each. The girls go up to their rooms.

A few minutes later, a triple frees up, which costs just $25. So the manager, to be a nice guy, decides to move the girls into the triple and refund the $5 difference. He sends the bellboy up to tell the girls of their good fortune and move them into the triple.

While riding up in the elevator, the bellboy thinks to himself, “How can the girls split the $5? $5 doesn’t divide by 3 evenly. I’ll make it easier for them: I’ll give them just $3 — and keep $2 for myself.” So he gave the girls $3 and moved them into the triple.

Everybody was happy. The girls were happy to get refunds. The manager was happy to be a nice guy. And the bellboy was happy to keep $2.

Now here’s the problem: each girl spent $10 and got $1 back, so each girl spent $9. So altogether, the girls spent $9+$9+$9, which is $27, and the bellboy got $2. That makes $29. But we started with $30. What happened to the extra dollar?

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