Faculty Advisor

Dr. David Sher


In this project we studied the mathematical concept of the Frobenius number and some curious patterns that come with it. One common example of the Frobenius number is the Coin Problem: If handed two denominations of coins, say 4¢ and 5¢, and asked to create all possible values, we will eventually find ourselves in a position where we can make any value. With 4¢ and 5¢ coins, we can create any value above 11¢, but not 11¢ itself. So, that makes 11 the Frobenius number of 4 and 5. What we explore in this paper is a pattern we call Frobenius symmetry: when all non-negative integers below the Frobenius number can be paired up such that one number is attainable, and the other is not. We looked at sets of two and three numbers and arrived at results about both.