Three people check into a hotel. The clerk tells them that the bill for their stay is $30, so each person pays the clerk $10. The clerk puts the money in the cash register.

Question

Later that night, the clerk realizes that he made a mistake and should have only charged the three guests $25. He pulls $5 in one dollar bills out of the register and tells the bellhop to return the money to the guests.

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On the way to the room, the bellhop realizes that he cannot split the money evenly between the three people. As the guests don't know that they were charged the incorrect amount for their room, the bellhop decides to simply give them $1 each and pocket the extra $2 as a tip. Each guest gets $1 back, so they each paid $9 for their room, totaling $27. The bellhop kept $2, and $27 + $2 = $29.

But the guests originally handed over $30. What happened to the missing dollar?

Answer 1

The missing dollar is a result of flawed reasoning in the explanation. To clarify:

1. Initially, the guests paid $30 total for the room, each paying $10.
2. The clerk should have only charged them $25, so $5 needed to be returned to the guests.
3. The bellhop gives each guest $1 back, meaning they paid $9 each, totaling $27.
4. The remaining $2 that the bellhop kept should be added to the $27 the guests paid, not subtracted.

Therefore, $27 (amount guests paid) + $2 (amount bellhop kept) = $29, which accounts for the total money. The missing dollar is just a mathematical distraction and is not actually missing.