# Problem of the Week: Spring 2024, Number 2

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.

Solutions Due: Saturday, February 3, 5:00 p.m.

Send solutions to bkennedy@gettysburg.edu.

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.

A Rock-Solid Investment

Consider the following game. 10 rocks are in a bucket, and each rock has a positive whole number from 1 to 10 painted on it (each rock has a different number). You may “buy” up to 10 rocks at a price of three dollars each. If you buy k rocks, you then draw k rocks at random out of the bucket. You will then receive m dollars, where m is the largest number appearing on any of the rocks you chose.

What’s the best number of rocks to buy? Explain. Can you generalize?

Author: Gettysburgian Staff