Problem of the Week: Rationality at Dessert
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.
This is the final P.O.W. contest of the semester.
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 firstname.lastname@example.org. This problem was posted on Monday, November 29 and solutions are due on Friday, December 3 by 5:00 p.m.
Four friends A, B, C, and D have a perfectly square, 10-inch × 10-inch cake to share. They decide to divide the cake in the following way: A will make a vertical cut, wherever she chooses, all the way across the cake. Then B will make a horizontal cut, wherever he chooses, all the way across the cake. There will now be four pieces of cake. D and C will choose their pieces first; then B will choose, and finally A will take the remaining piece.
Assuming that each friend will take the largest piece of cake possible (and knows that everybody else will take the largest piece of cake possible), how much cake will everybody get?