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