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Anniversary math problem

07/31/03 12:00AM By Dan Rockmore
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(Host) Commentator Dan Rockmore examines a math problem today that may - or may not - hold the key to finding one's own true love.

(Rockmore) My parents recently celebrated their 42nd wedding anniversary and as often happens at our family celebrations, we goaded my Dad into telling the story of how he met my Mom.

It was a wintry night in the early 1950s in New York City and he and his grad school buddy Ted were throwing a party. Ted was quite a ladies man and he had invited all the women he knew to his Upper West Side apartment near Columbia University for an evening of fun with some aspiring physicists! Talk about getting
physical!

By my Dad's account the party was a great success. He wanted to meet a nice girl and settle down, so ever the scientist, he proceeded around the room in an orderly fashion and by evening's end he had accumulated a list of the names and phone numbers of ten engaging and eligible bachelorettes. But now he had a new problem: how to find his true love among the delightful ladies on this list?

Had my Dad been a mathematician and not a physicist, he might have known that the problem he now faced was a variation on an old, old math problem, which years ago was called the *secretary problem*. It goes like this: Suppose we have a list of ten applicants all competing for the same job. One by one, they come for an interview. If a candidate is offered the job, then the search is over and no one else is interviewed. Otherwise, the candidate is not offered the position, but then is immediately snapped up by a competing company! Under these conditions, how do we maximize the chance of getting the best person for the job?

Now one approach might be to just take the first one you like, but you may then miss out on an even better person interviewing later! On the other hand, you may pass over a good one, hoping for someone better, and that may never happen!

It turns out that the best strategy is somewhere in etween these extremes: interview the first five candidates, but *don't* offer the job to *any* of them. Then, starting with candidate six, offer the job to the first candidate who is *better* than all of those first five - or if none of them are, take the last candidate. This strategy gives you about a one in four chance of getting the best person on the list.

Luckily for yours truly, every once in a while my Dad the scientist throws caution to the wind and lets his heart rule his head. My Mom was number two on his list, and after a less than great date with bachelorette number one, he and my Mom went out and that was it - his search was over.

I guess that it just goes to show, that maybe "doing the math" isn't always the greatest strategy, especially when you're looking to be fruitful and multiply.

From Hanover New Hampshire, this is Dan Rockmore.

Dan Rockmore is a professor of mathematics and computer science at Dartmouth College. He spoke from our studio in Norwich.
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