# All time classic problem

lionel
Posers and Puzzles 08 Mar '03 20:05
1. 08 Mar '03 20:05
Three men go to a hotel and ask how much for a room. Manager says \$30. Each man pays \$10. After awhile the manager decides he charged to much. He then gives the bellhop \$5 and says to give it back to the men. On the way to the room, the bellhop decides to keep \$2. He then gives each man \$1 back. That makes each man paying \$9. Three times 9 equals 27 that the men paid. 2 that the bellhop kept plus 27 that the men paid adds up to 29. Where is the other dollar?
2. 08 Mar '03 20:44
Originally posted by lionel
Three men go to a hotel and ask how much for a room. Manager says \$30. Each man pays \$10. After awhile the manager decides he charged to much. He then gives the bellhop \$5 and says to give it back to the men. On the way to the room, the bellhop decides to keep \$2. He then gives each man \$1 back. That makes each man paying \$9. Three times 9 equals 27 that the ...[text shortened]... aid. 2 that the bellhop kept plus 27 that the men paid adds up to 29. Where is the other dollar?
If you write it down there is no missing dollar, there can not be.

25+3 is 28, bell boy gets 2 =30

25 does not divide down by 3, i think that is where the issue is - you need to add on to 25 not take off 30?

Andrew
3. Omnislash
Digital Blasphemy
09 Mar '03 02:11
Agreed. The problem with the equation is that the end question multiplies instead of using addition/subtraction. Because the bell boy took the 2 off from the 30 the multilples hold a different percentile value for each guest versus the initial sum. The numerical values are sensitive to the sequence of events, and thusly the end questions use of multiplication is faulty.
4. 09 Mar '03 18:09
Originally posted by Omnislash
Agreed. The problem with the equation is that the end question multiplies instead of using addition/subtraction. Because the bell boy took the 2 off from the 30 the multilples hold a different percentile value for each guest versus the initial sum. The numerical values are sensitive to the sequence of events, and thusly the end questions use of multiplication is faulty.
Omnislash

Have you ever come across the Plain English Campaign?

Here's a link to the website...

www.plainenglish.co.uk

Ta
Tim
5. Acolyte
09 Mar '03 21:481 edit
Originally posted by lionel
Three men go to a hotel and ask how much for a room. Manager says \$30. Each man pays \$10. After awhile the manager decides he charged to much. He then gives the bellhop \$5 and says to give it back to the men. On the way to the room, the bell ...[text shortened]... lus 27 that the men paid adds up to 29. Where is the other dollar?
The three men are each down \$9. The manager is up \$25. The bellhop is up \$2. No problem.

If you want to know where the \$30 are, there is no single 'other dollar'. Instead the men got a \$3 refund, which you've ignored, and you've double-counted the bellhop's \$2 (once as part of the payment, once as what the bellhop keeps). Through these two errors in the arithmetic you arrive at a spurious 'missing dollar'.

I know Omnislash got here first but I think I've explained it better. ðŸ˜› I don't know what Omnislash means by the money being sensitive to the sequence of events though... ðŸ˜•

PS Ignore this. Latex bishop got there before both of us and gave a perfectly good explanation.
6. Omnislash
Digital Blasphemy
09 Mar '03 21:551 edit
A vocabulary is a horrible thing to waste. ðŸ˜‰
The real props do have to go to latex bishop. ðŸ™‚
7. 10 Apr '03 04:06
Originally posted by lionel
Three men go to a hotel and ask how much for a room. Manager says \$30. Each man pays \$10. After awhile the manager decides he charged to much. He then gives the bellhop \$5 and says to give it back to the men. On the way to the room, the bellhop decides to keep \$2. He then gives each man \$1 back. That makes each man paying \$9. Three times 9 equals 27 that the ...[text shortened]... aid. 2 that the bellhop kept plus 27 that the men paid adds up to 29. Where is the other dollar?
You are misleADIONG YOUR audience - don't add the two dollars bus subtract it, then you have 25 + 2 or 27 - 2, which comes out equal. See ?
8. 12 Apr '03 09:19
Originally posted by suneclipse
You are misleADIONG YOUR audience - don't add the two dollars bus subtract it, then you have 25 + 2 or 27 - 2, which comes out equal. See ?
So where did the missing dollar go?