City-Data Forum Do numbers lie? (refund, money, paying, cash)
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09-16-2011, 07:33 AM
 Location: San Diego California 6,796 posts, read 7,158,996 times Reputation: 5191

A riddle began back during the last depression that I have not heard for some time. I thought it would be fun to try it on some people who may not heard it.

Three men check into a hotel.
The manager charges each man \$10 for his room.
After a while, the manager has second thoughts about the rate he had charged the men and decides to give them a refund.
He calls the bellhop and gives him \$5 instructing him to return it to the customers.
The bellhop had difficulty figuring how to divide \$5 by three people so he decided to give each of the men \$1 each and keep the other \$2 for himself.
So now, after the refund, each customer has paid \$9 (3X\$9= \$27)
The bell boy has kept \$2, \$27+\$2=\$29
Where is the missing \$1?

09-16-2011, 08:24 AM
 2,515 posts, read 1,957,292 times Reputation: 362
Quote:
 Originally Posted by jimhcom A riddle began back during the last depression that I have not heard for some time. I thought it would be fun to try it on some people who may not heard it. Three men check into a hotel. The manager charges each man \$10 for his room. After a while, the manager has second thoughts about the rate he had charged the men and decides to give them a refund. He calls the bellhop and gives him \$5 instructing him to return it to the customers. The bellhop had difficulty figuring how to divide \$5 by three people so he decided to give each of the men \$1 each and keep the other \$2 for himself. So now, after the refund, each customer has paid \$9 (3X\$9= \$27) The bell boy has kept \$2, \$27+\$2=\$29 Where is the missing \$1?
The math was set up wrong. starting with the total amount of money \$35 each man had \$10 and got \$1 back leaving two extra for the bellhop. 30-3=27 5-3=2 so 27+3+2=35 you aren't trying to add up to 30 you are trying to add up to 35.

09-16-2011, 08:27 AM
 Location: Ohio 3,439 posts, read 5,989,095 times Reputation: 2694
I don't know where you are getting the \$35 but you are right about the math being wrong it is \$25+\$3(returned to the guys)+\$2(tip)= \$30

09-16-2011, 08:31 AM
 2,515 posts, read 1,957,292 times Reputation: 362
Quote:
 Originally Posted by Trackwatch I don't know where you are getting the \$35 but you are right about the math being wrong it is \$25+\$3(returned to the guys)+\$2(tip)= \$30
Each man contributed \$10 and the owner contributed \$5 for a total of \$35. \$5 was to be given to the other three people. But only 3 was leaving 2 for the bellhop

09-16-2011, 08:52 AM
 Location: Martinsville, NJ 6,175 posts, read 12,754,906 times Reputation: 4017
Quote:
 Originally Posted by newonecoming2 Each man contributed \$10 and the owner contributed \$5 for a total of \$35. \$5 was to be given to the other three people. But only 3 was leaving 2 for the bellhop
The total is \$30, not \$35. Imagine the cash register was empty before these guys arrived with their \$30. The \$5 "contributed" by the owner is just a refund from the original \$30. Since each man got back a dollar, they have now paid \$9 each, for a total of \$27. That \$27 was divided between the owner, who got \$25, and the bellhop, who got \$2, and ought to be fired & prosecuted as a thief.

09-16-2011, 08:54 AM
 Location: Victoria TX 42,660 posts, read 85,391,454 times Reputation: 36620
Each man started out paying \$10, which makes \$30. The manager only wanted \$25, so he took a fin out of the till. So each man got a dollar back, and paid \$9. That's \$27. Of that, the manager got \$25, the bellboy got \$2. The bellboy kept \$2, from the total of \$27 that the occupants paid, and the manager got the other \$25.. What's the problem?

09-16-2011, 09:07 AM
 2,515 posts, read 1,957,292 times Reputation: 362
Quote:
 Originally Posted by Bill Keegan The total is \$30, not \$35. Imagine the cash register was empty before these guys arrived with their \$30. The \$5 "contributed" by the owner is just a refund from the original \$30. Since each man got back a dollar, they have now paid \$9 each, for a total of \$27. That \$27 was divided between the owner, who got \$25, and the bellhop, who got \$2, and ought to be fired & prosecuted as a thief.
The owner took \$5 out of his "pocket" The till what ever and gave to the three guests of that 5 2 were kept by the bellhop. It doesn't matter where the 5 came from. three \$10 dollar bills and a \$5 dollar bill, total 35 dollars in play \$30 going one way and 5 going the other. so where was the math error in the original riddle?

09-16-2011, 09:23 AM
 Location: Martinsville, NJ 6,175 posts, read 12,754,906 times Reputation: 4017
Quote:
 Originally Posted by newonecoming2 The owner took \$5 out of his "pocket" The till what ever and gave to the three guests of that 5 2 were kept by the bellhop. It doesn't matter where the 5 came from. three \$10 dollar bills and a \$5 dollar bill, total 35 dollars in play \$30 going one way and 5 going the other. so where was the math error in the original riddle?
I find that a silly way to look at it.

The three men originally paid \$10 each, and then got a refund of \$1 each, for a total expenditure of \$27. Do you agree with that?

Of that total, the owner got \$25, and the belhop got \$2. No argument with that, is there?

The "error" in the riddle lies in adding the \$2 that the bellhop kept to the \$27 the customers paid. That's a mistake because the bellhop's \$2 is PART OF the customer's \$27 expenditure, not any kind of addition to it. The total spent by the three customers must equal the total gained by the owner & the bellhop.

The math problem should be (\$Paid by man1 + \$Paid by man2 + \$Paid by man3) = (\$gained by owner + \$gained by thieving bellhop).

Why would you want to say that the \$5 the bellhop was supposed to give the customers is somehow a DIFFERENT \$5, and have to add it into the equations, complicating matters?

09-16-2011, 09:29 AM
 Location: Martinsville, NJ 6,175 posts, read 12,754,906 times Reputation: 4017
Quote:
 Originally Posted by newonecoming2 The math was set up wrong. starting with the total amount of money \$35 each man had \$10 and got \$1 back leaving two extra for the bellhop. 30-3=27 5-3=2 so 27+3+2=35 you aren't trying to add up to 30 you are trying to add up to 35.

There's another math error in your solution, by the way. The part I put in red above is clearly wrong. 27+3+2 = 32, not 35. And what would be the point in adding the total the men paid after the refund, plus the amount they were refunded, plus the amount the bellhop stole? the last 2 numbers in that equation are PART of the first number.

09-16-2011, 09:32 AM
 2,515 posts, read 1,957,292 times Reputation: 362
Quote:
 Originally Posted by Bill Keegan There's another math error in your solution, by the way. The part I put in red above is clearly wrong. 27+3+2 = 32, not 35. And what would be the point in adding the total the men paid after the refund, plus the amount they were refunded, plus the amount the bellhop stole? the last 2 numbers in that equation are PART of the first number.
True enough My bad so much for doing math in mny head early in the morning without having had enough to eat.
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