Student Research Projects

Linear Diophantine Equations versus the Penny

Student Laura Robusto, '16
Tyler Searcy, '16
Faculty Mentor(s)
Department Mathematics
Course Math 489: Research in Mathematics


Have you ever wondered how many ways there are to make a dollar? Sure, you can use 4 quarters, or 10 dimes, or 100 pennies. But using any combination of coins, how many ways are possible? Are there any combinations that use exactly 17 coins, or 98 coins? In this presentation, we investigate the number of ways of combining n coins in our monetary system to make one dollar for each 1 < n < 100 and discuss the necessity and efficiency of the coins in our monetary system. Using linear Diophantine equations, original methods, and previously known algorithms for change-making problems, we will build a case for abolishing the penny.


NSM Summer Research Grant
UR Conference Funds


MAA MathFest 2015