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The Traveling Businessman Dilemma

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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
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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
Check out our web site! http://mathforum.org/dr.math/
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