Problem of the Week: Turning Things Over
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, October 15 and solutions are due on Friday, October 22 by 5:00 p.m.
THE PROBLEM:
Professor Hult and Professor Kennedy are playing a game. Professor Hult will place 100 coins in a row, some with heads facing up and some with tails facing up. Professor Kennedy will turn over 99 of the coins, then 98 of the coins, then 97 of the coins, and so on, finally turning over two of the coins, then one of the coins.
If, at the end, all the coins are facing the same direction (either all heads facing up or all tails facing up), Professor Kennedy wins; otherwise, Professor Hult wins.
How can Professor Hult arrange the coins to guarantee that she wins? Answer, and explain.
HINT: Try playing “smaller” versions of the game with your friends. If you use four coins, you should turn over 3, then 2, then 1; if you use five coins, you should turn over 4, then 3, then 2, then 1.
