Math 450 Presents "Cups and Downs"

 


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.

 
 
 
 

 

 

 

Math 450 Presents "Fractals and Mysterious Triangles"

Cards of three colors are dealt in a row of size n. The cards are then continually dealt into rows above each other of size n-1, n-2, n-3, … until the row of size 1 is reached. The cards must be placed following 2 rules. One, if two cards, adjacent cards, from the previous row share the same color, the card above them must be that color as well. Two, if two adjacent cards are different colors, the card above them must be of the third color. These cards form a “mysterious triangle.” We want to know how we could predict the color of the apex card of the triangle without dealing out all the cards. Using Sierpinski Triangles, mod 3 arithmetic, and fractals, we will figure out exactly that.

Jones, M. A., Mitchell, L., Shelton, B. “Fractals and Mysterious Triangles.” Math Horizons.

      September 2015. pp 22-25.

 

Math 450 Presents

"Fractals and Mysterious Triangles"

by: Shelbey Linder

Tuesday, October 20, 2015, 1:40 p.m.

in Patterson 301

 

Come join us! All are welcome.



Math 450 Seminar Presents "Mathematics for Gamers!"

The problem discussed in this article begins with the introduction of zombies in the video game Call of Duty: Black Ops. However, the solution to this problem is a mathematical problem that needs a solution as well. There are four dials placed among four levels of a building, and the solution of this problem requires a certain algorithm of turning the dials to read in order 2, 7, 4, and 6.

In Math Horizons, February 2014 edition, Heidi Hulsizer tackles the problem presented to her in one of the video games she plays regularly. After careful consideration she discovered two ways to mathematically solve this Easter egg. The first way is with an algebraic approach, while the second deals with a matrix approach.  Who knew video games involved so much thinking!

Math 450 Presents

"Mathematics for Gamers!"

by: Jacob Ackerman

Tuesday, October 13, 2015, 1:40 p.m.

in Patterson 301

Come join us! All are welcome.

Math 450 Seminar Presents "The Multiplication Game!"

The game is simple, the dealer hands you a random number that you cannot see, and you then enter your own integer. If the first digit of the product is between 4 and 9 you win! If the first digit of the product is 1, 2, or 3 the dealer wins. The odds seem tempting, would you take them?

In an article from the April 2010 edition of Mathematics Magazine, Kent E. Morrison analyzes this game and discovers what the odds are and how we need to apply game theory to the problem in order to completely solve the total expected outcome of this game. Although this may seem like a very straight forward problem, we will learn that a lot goes into solving this simple multiplication game.

 

Math 450 Seminar Presents

"The Multiplication Game"

by: Alexander Lillich

Tuesday, October 6, 2015, 1:40 p.m.

in Patterson 301

 

Come join us! All are welcome.