Mathematics Problem of the Week

Fall 2004

POW 3: A Three Switch Light

Suppose that a traffic light has been wired by a mathematical electrician so that it is controlled by three switches and each switch has three positions.

Here are some axioms about this traffic light:

A. When all three switches are up (0,0,0) the light is Red (see diagram).

B. If you then move the first switch to the right, i.e. (1,0,0), the light turns yellow.

C. Anytime you change all three switches, the light will change color.

D. The color depends only on the positions of the switches, not how you got there.

What color is the traffic light for each of the switch configurations below?

Justify your answers.

(a)

(b)

Due Friday, September 17^th, at Noon.

Solutions should be submitted to Dr. Patti Lock’s mailbox in the Math office or sent via e-mail to plock@stlawu.edu

Presentation counts! The prize-winning entry will be selected from all correct submissions, based on the clarity, creativity and elegance of the solution.

Look for the SLU POW on the Web at http://it.stlawu.edu/~math/activities/