Problem of the Week: Dancing

Editor’s Note: The Department of Mathematics at Gettysburg College hosts a problem of the week challenge to determine each semester’s Paul Mugabi problem-solving award recipient(s).  Each week’s entries are scored by a faculty judge, and winner(s) from each week will receive a Problem Of the Week (P.O.W.) button.  The Gettysburgian is not involved in or responsible for accepting or evaluating students’ submissions to this contest.

Problem of the week

THE RULES:

The contest is open to all Gettysburg College students. Up to three people may work together on a submission. Make sure your name is on your submission and that any sources are properly cited. Send solutions to bkennedy@gettysburg.edu.  This problem was posted on Friday, September 10 and solutions are due on Friday, September 17 by 5:00 p.m.

THE PROBLEM: 

Six friends A, B, C, D, E, and F want to practice their ballroom dancing. They will play five songs; during each song, every person will dance with exactly one other person. Write down a schedule for who dances together on each song, and design your schedule so that no person dances with the same person twice.

Optional extra challenge: How many different such schedules are possible?

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Author: Gettysburgian Staff

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