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The Traveling Businessman Dilemma

Date: 04/09/98 at 09:32:55
From: david tucker
Subject: Where's the 30th dollar?

Three guys are on a business trip and need a place to stay for the 
night. They see a hotel for $30 dollars a night and decide that would 
be perfect - $10 each. They go in and pay and as they are walking 
out, the manager realizes he knows one of the guys and asks the 
bellboy to take $5 back to them. He realizes he can't split $5 three 
ways so he gives back $1 dollar to each guy and keeps a $2 tip. 

Now each guy has paid $9 instead of $10, and the bellboy keeps 2 of 
the dollars. So 9(dollars)x 3(guys)= 27 dollars plus the bellboy's 
2 dollars, a total of $29. Where's the 30th dollar?  

I myself and others can't figure this out. I believe it should work 
out the way I have written it. 

Thanks for your time,
David Tucker

Date: 04/09/98 at 11:35:24
From: Doctor Rothman
Subject: Re: Where's the 30th dollar?

Hi. The first time I read it, I didn't get it either. But then I 
realized that you just have to be REALLY careful about how you count 
the dollars. 

Let's give each of the $30 a number from 1-30, keep track of each 
individual dollar, and see how the problem works. 

Dollars numbered 1-30 are given to the manager. Then he wants to give 
$5 back, so he keeps the dollars numbered 1-25, and gives numbers 
26-30 to the bellboy in the form of a five dollar bill. The bellboy 
splits up the five to get 5 one's: numbers 26, 27, 28, 29 and 30.  
He gives numbers 26, 27 and 28 to the customers and keeps numbers 29 
and 30 for himself.

-Doctor Rothman,  The Math Forum
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