Math Problem of the Week

Department of Mathematics Gettysburg College.

The Math Problem of the Week Contest

Spring 2022, Number 11

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.

Weekly winners will receive a POW victory button, and the best-performing students of the semester will receive the Paul Mugabi problem-solving award.

Problem posted: Friday, April 15

Solutions Due: Friday, April 22 5:00 p.m.

Send submissions to: bkennedy@gettysburg.edu.

This is the last P.O.W. of the semester.

Futility Rocks

I have just been hired to work in Earl Eccentric’s rock garden, where there
is one pile containing A rocks and another pile containing B rocks.

Here is my job. At the beginning of every hour, I will calculate the total
number T of rocks in the two piles together, and 

if T is even, I will move T /2 rocks from the larger pile to the smaller
pile;

if T is odd, I will choose one rock (from either pile) to throw away into
the bushes.

My task will be complete when the two piles have the same number of
rocks; after that, I do not have to move any more rocks.

QUESTION: For which values of A and B is it possible for me to complete
my task? Answer, and explain.