Mathematics Problem Of the Week

Spring 2006

POW #1

Colored Corners

Suppose that we wished to color each vertex of a geometric figure with colors chosen from among red, yellow, blue or green. Each vertex gets just one color and the same color can be used for more than one vertex. Two colorings are considered different if there is no rotation or reflection of the figure that makes them look the same.

(a) In how many different ways could we color the vertices of an equilateral triangle?

(b) How many different colorings for the vertices of a square?

Give clear justifications for your answers in each case.

Due Friday, February 3^rd Noon

Solutions should be submitted to Dr. R. Lock's mailbox in the Math office or sent via e-mail to rlock@stlawu.edu.