Say three men decide to get a hotel for the night. The price is 30 dollars, ten per person. After they go to their room, the desk clerk decides that he over charged the fellows, and sends the bell hop up to give them 5 dollars back. The bell hope figures it is quite hard to split 5 dollars between 3 people, so he gives them a dollar each, and pockets the other two dollars. Here is my problem:
if they each get a dollar back, they only payed 9$ apiece for the room
9x3=27+ the 2 the bellhop kept=29. Where did the other dollar go? I know this is not worded well, but this question has been bugging me for some time, thanks for the help
You’re combining apples and oranges. Here is where the $30 went:
$25 to the hotel
$3 back to the men
$2 to the bellhop
Yes, they “paid” $27 for the room, but that’s because the bellhop kept $2 that they were supposed to get back. The $2 is part of what they “paid” – you can’t count it twice. They “paid” $27 and got $3 back – there’s the $30.
The word “chestnut” comes to mind! My dad used this exact same riddle to amaze and befuddle my sisters and me forty years ago. In fact, the riddle is a classic example of how the listener can be misled purely by the presentation of the riddle itself. The actual math could hardly be simpler.
In this case, the listener is led to the erroneous assumption that the two bucks the bellhop pocketed are somehow separate from the $27 the three men paid. In fact, the $2 is part of the $27, and represents the difference between the $25 the clerk intended to charge the men, and what the men actually wound up paying.
In other words, 27 (the 25 charged by the clerk plus the 2 kept by the bellhop) + 3 (the actual refund the three men received) = 30. The dollars are all there, but the teller of the riddle presents it in a misleading manner.
Incidentally, my dad used to cite this riddle as an example of how “numbers lie,” and today, at age 75, he still believes that, despite having it explained countless times.