Dr. James Hamblin, Shippensburg University, will present "A Variation on the Money-Changing Problem" on Tuesday, April 10th at Noon in Tome 115. Free pizza and everyone welcome to attend!
Abstract: Suppose you move to a country that has 5-cent, 12-cent, and 26-cent coins. Which denominations can you make change for? Which denominations can you *not* make change for? For those denominations that you can make change for, how many ways are there to do it? This number is called the denumerant, and has been studied extensively. In this talk we will investigate the maximal denumerant, which counts the number of ways to make change for an amount using the largest possible number of coins.
Here's a challenge to get you started thinking about this problem. Using 5, 12, and 26, find a number whose maximal denumerant is greater than 1. In other words, find an amount that you can make change for using the same number of coins in at least two different ways, and for which there is no other way to make change for it using more coins.