How many moves does it take to flip three pennies so that they're all showing the same face? How many moves does it take to flip three cups so they are all upside down when one move inverts two cups at a time?

The article Cups and Downs, found in the January 2012 issue of the College Mathematics Journal, looks at the state diagrams for each of these "magic tricks" to determine the maximum number of moves needed to solve each problem. using matrices, the cups problem is extended to see how many moves are required to invert

*n*number of cups if each move inverts exactly*m*cups at a time. Although the solution seems simple, it turns out to be surprisingly complicated.
Stewart, Ian. "Cups and Downs."

*The College Mathematics Journal*January 2012: 15-19. Print.**Math 450 Presents**

**"Cups and Downs"**

**by: Emily Marconi**

**Tuesday, November 3, 2015**

**1:40 p.m.**

**in Patterson 301**

**Come join us! All are Welcome.**