By Department of Mathematics
Deadline: 11:59 PM on Sunday, Sept. 29
The Rules:
The contest is open to everyone. Individuals or teams of at most three members may submit solutions. Do not discuss the problem with anyone other than members of your team. You may use any source, written or electronic, but all sources must be properly cited. You may use any computational tools. Your solution will be graded on a 0–4 point scale. All your assertions must be completely and fully justified. At the same time, you should aim to be as concise as possible; avoid overly lengthy arguments and unnecessary components. Your grade will be based on both mathematical accuracy and clarity of presentation. Either send your solution to bbajnok@gettysburg.edu or put it in Bela’s departmental mailbox by the above deadline. Consistently successful participants will receive the Paul Mugabi Mathematics Problem Solving Award.
The Problem:
In the dice game of GettysHog, the object is to be the first player to score 25 or more points. It is played with a collection of 6-sided dice that each have 5 sides that are orange and 1 side that is blue. Each turn, a player takes any number of such 6-sided dice and rolls them simultaneously. If any blues are rolled, the player’s score remains the same. If no blues are rolled, the player increases their score by the number of dice rolled. For which number(s) of dice rolled is a player expected to maximize their score gain on a turn? What is the expected maximal score gain per turn?
This problem was contributed by Professor Todd Neller.
