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.
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 email@example.com. This problem was posted on Friday, September 10 and solutions are due on Friday, September 17 by 5:00 p.m.
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?