## Frank Morgan's Math Chat |

MAY 17, 2001

A few years ago I bought a candy bar at the concession stand in a movie theater. I paid with a $20 bill. My change was a thick wad of bills accompanied by the apology, "Sorry for all the singles, but I only have one Ten left and I want to save it in case I need it later."

Does this make any sense? What is the best strategy for making change at a concession stand?

**Answer.** Most readers agree with Joseph DeVincentis:

"No, it doesn't make any sense. If there was ever a time the concessioneer needed the Ten, it was right then."

and John M. Sullivan:

"No. It's ridiculous! (Unless you're saving the Ten for a customer who puts up more of a fight!)"

On the other hand, David Feuer suggests that it could make sense to save the Ten in case someone comes along with a Fifty later. Joe Shipman observes that cash registers have drawers of finite size, and if you have too many Ones you'll want to get rid of them in preference to larger bills. DeVincentis similarly suggests that you might want to give out the smaller denominations to avoid accumulating so many of them. Math Chat suspects that the concessioneer has to stay late every day counting up piles of Ones and does everything he can to get rid of them earlier.

**Questionable Mathematics.** Recent email attributes the following story to
Dilbert cartoonist Scott Adams:

The other day at the gas station, while waiting in line to pay for my gas, I commented to another customer how expensive gasoline had become. Her reply was, "You know, it doesn't really affect me; I always put in twenty dollars every time I gas up."

Reminds me of the time my mom was pleased to buy some stamps just before the postage rate went up.

Readers are invited to submit more examples of questionable mathematics.

**New Challenge.** In fifty years, what will be the fastest commercial
transportation from New York to Beijing?

Copyright 2001, Frank Morgan.

Send answers, comments, and new questions by email to
Frank.Morgan@williams.edu, to be eligible for* Flatland *and other book
awards. Winning answers will appear in the next Math Chat. Math Chat
appears on the first and third Thursdays of each month. Prof. Morgan's
homepage is at www.williams.edu/Mathematics/fmorgan.

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