Deciding the Guest List for an Important Party
Let’s say you’re planning your next party and agonizing over the guest list.
To whom should you send invitations?
What combination of friends and strangers is the right mix?
It turns out mathematicians have been working on a version of this problem for nearly a century.
Depending on what you want, the answer can be complicated.
Our book, ‘The Fascinating World of Graph Theory,’ explores puzzles like these and shows how they can be solved through graphs.
A question like this one might seem small, but it’s a beautiful demonstration of how graphs can be used to solve mathematical problems in such diverse fields as the sciences, communication and society.
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A puzzle is born
While it’s well-known that Harvard is one of the top academic universities in the country, you might be surprised to learn that there was a time when Harvard had one of the nation’s best football teams.
But in 1931, led by All–American quarterback Barry Wood, such was the case.
That season Harvard played Army.
At halftime, unexpectedly, Army led Harvard 13–0.
Clearly upset, Harvard’s president told Army’s commandant of cadets that while Army may be better than Harvard in football, Harvard was superior in a more scholarly competition.
Though Harvard came back to defeat Army 14-13, the commandant accepted the challenge to compete against Harvard in something more scholarly.
It was agreed that the two would compete – in mathematics.
This led to Army and Harvard selecting mathematics teams; the showdown occurred in West Point in 1933.
To Harvard’s surprise, Army won.
The Harvard–Army competition eventually led to an annual mathematics competition for undergraduates in 1938, called the Putnam exam, named for William Lowell Putnam, a relative of Harvard’s president.
This exam was designed to stimulate a healthy rivalry in mathematics in the United States and Canada.
Over the years and continuing to this day, this exam has contained many interesting and often challenging problems – including the one we describe above.
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