Spring 2010 Problem 2: Rolling, rolling, rolling...

A pencil has a pentagonal cross section with the Centenary logo printed on one of the five sides. You roll the pencil — what's the probability that the logo is visible from above?

Solution

Roland Womack gave the bonus point for the best explanation:

Since the shape of the cross section of the pencil is a pentagon, 2 of the 5 sides are visible from directly above when the pencil is at rest. If the Centenary logo is printed on only one side of the pencil, rolling the pencil and allowing it to come to rest will mean that there is a 2 out of 5, or 40%, chance that the logo will be visible from directly above.

Nicki Escott got the bonus point for the first correct answer. Also earning the base two points were: Charles Madden, Robert Poole, Christopher Youngblood, Josh Pena, and Jacob Jennings. Correct non-student answers came from Kathryn Applegate, Don Dinnerville, and Micah Strange. The problem came from Peter Winkler's book Mathematical Mind-Benders.

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Solution