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.
Solutions Due: Saturday, March 2, 5:00 p.m.
Send solutions to bkennedy@gettysburg.edu. 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. Weekly winners will receive a POW victory button, and the best-performing students of the semester will receive the Paul Mugabi problem-solving award.
Lonely Puppies!
Evil villain Dr. Horrible descends on a dog park where 10 puppies and their 10 owners are playing. Dr. Horrible seizes all the puppies and then hands each puppy back to a random owner! (Each owner gets exactly one puppy back, at random — maybe their own). With a malicious chuckle, Dr. Horrible then says: “I will permit up to eight puppy-trades between pairs of owners — no more. Then you must all go home with whatever puppy you have.”
What is the probably that the 10 owners (assuming they work optimally together, subject to Dr. Horrible’s rules) will all go home with their own puppies?
