Problem of the Week: Sealdle
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 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, February 25 and solutions are due on Friday, March 4 by 5:00 p.m.
THE PROBLEM:
I agreed to take care of my uncle’s four trained seals while he went on vacation. The seals’ names are A, B, C, and D; ordinarily, they wear signs around their necks with their names on them.
When the seals arrived at my house in their special water-tank van, the signs were all jumbled up on the passenger seat. I want to figure out which seal is which. Fortunately, the seals know a trick: if I hang one sign around each seal’s neck and then blow my whistle, the seals wearing their own signs will bark (and the seals not wearing their own signs will stay silent).
Describe a trial-and-error procedure that will allow me to get each sign on the correct seal by performing this trick repeatedly. Tell me the maximum number of repetitions I might possibly need (with explanation); your objective is to make this number as small as possible.
