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Quick Calculations in Everyday Life
(Section 7.8 of
Programming Pearls)

The publication of this column in Communications of the ACM provoked many interesting letters. One reader told of hearing an advertisement state that a salesperson had driven a new car 100,000 miles in one year, and then asking his son to examine the validity of the claim. Here's one quick answer: there are 2000 working hours per year (50 weeks times 40 hours per week), and a salesperson might average 50 miles per hour; that ignores time spent actually selling, but it does multiply to the claim. The statement is therefore at the outer limits of believability.

Everyday life presents us with many opportunities to hone our skills at quick calculations. For instance, how much money have you spent in the past year eating in restaurants? I was once horrified to hear a New Yorker quickly compute that he and his wife spend more money each month on taxicabs than they spend on rent. And for California readers (who may not know what a taxicab is), how long does it take to fill a swimming pool with a garden hose?

Several readers commented that quick calculations are appropriately taught at an early age. Roger Pinkham wrote

I am a teacher and have tried for years to teach ``back-of-the-envelope'' calculations to anyone who would listen. I have been marvelously unsuccessful. It seems to require a doubting-Thomas turn of mind.

My father beat it into me. I come from the coast of Maine, and as a small child I was privy to a conversation between my father and his friend Homer Potter. Homer maintained that two ladies from Connecticut were pulling 200 pounds of lobsters a day. My father said, ``Let's see. If you pull a pot every fifteen minutes, and say you get three legal per pot, that's 12 an hour or about 100 per day. I don't believe it!''

``Well it is true!'' swore Homer. ``You never believe anything!''

Father wouldn't believe it, and that was that. Two weeks later Homer said, ``You know those two ladies, Fred? They were only pulling 20 pounds a day.''

Gracious to a fault, father grunted, ``Now that I believe.''

Several other readers discussed teaching this attitude to children, from the viewpoints of both parent and child. Popular questions for children were of the form ``How long would it take you to walk to Washington, D.C.?'' and ``How many leaves did we rake this year?'' Administered properly, such questions seem to encourage a life-long inquisitiveness in children, at the cost of bugging the heck out of the poor kids at the time.

Copyright © 1999 Lucent Technologies. All rights reserved. Mon 9 Aug 1999