Problem of the Week: Sand
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, September 24 and solutions are due on Friday, October 1 by 5:00 p.m.
THE PROBLEM:
I have three buckets of sand in my yard. Every day I choose the bucket with the most sand in it, and remove half of the sand from that bucket and throw it away. (If there is a tie for which bucket has the most sand, I randomly choose one of the buckets with the most sand.)
Every night, the raccoon who lives in my yard picks one of the buckets at random and doubles the amount of sand in that bucket. I wake up one morning and find that the three buckets have 12, 10, and 8 pounds of sand, respectively.
QUESTION: What’s the largest total pounds of sand there can be in the three buckets, for any day in the future? Give the answer, and tell me how you know.
Optional extra challenge: what if I wake up one morning and find a, b, and c pounds in the three buckets?
