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More than 100 correctly solve last Bailey Challenge
Editor’s note: The following is a regular Echoes mathematics problem provided by
Professor Emeritus Herb Bailey.
There were over 100 solvers for the summer problems. My keeping track of names, etc.,
falters with more than 30 solvers so forgive me for any tally errors. Several of the
younger solvers left the valuable locomotive boxed in by one of the cars and not available
for important jobs along the main track. I gave full credit since they should not be
expected to know the basics of railroading.
The great election will be decided by the time you read this and so I include an economics
(sort of) problem. Most of our economics problems will of course be solved by the
president elect. The second problem is taken from the recent Freshman Mathematics Contest
with about 20 top students competing. The winner this year was Miss Jess Gunn. About 1/4
of the contestants solved or almost solved the rolling card problem (Problem 2 below).
Problem 1. How many ways can you make change for a dollar using U. S. coins. Hint: the
answer is more than 280 and less than 300.
Problem 2. ABCD is a rectangle with sides AB = 1 and xxxxx. The rectangle rotates
clockwise around a vertex in contact with the table. If two vertices are in contact the
rotation is around vertex to right. The rectangle starts in the position shown and rotates
until A next contacts the table. What is the area of the region bounded by the path of A
and the table top?
Hint: Calculus is not needed and in fact not even wanted.
 
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