Math Problems of the Month
OSU-Marion
January 2006
Try your hand at these problems. Each month I will post a few of my favorite
math problems and puzzles. Some can be solved by algebra, some need some
clever intuition, some need a little elbow grease. I hope you enjoy them
as much as I do.
Submit answers to Dr. Maharry in MR 370 or at maharry@math.ohio-state.edu.
I will post the names of those who submit correct solutions outside my
door and on my web site.
- Find the smallest number (other than 1) in the sequence {1 , 11 ,
111 , 1111 , 11111, ...} that is a perfect square (like 25 or 36 or 144) or
prove that none of them are perfect squares.
- Sometimes the sum and the product of two numbers turns out to be
the same. Like 2+2 = 2 * 2 (which both equal 4) or (5/2 + 5/3) = (5/2 *
5/2) (which both equal 25/6). Describe all pairs of fractions that have this
property.
- A fruit salesman at an outdoor market has a double pan balance and
only three weights. But with his three weights he can weigh any whole number
of pounds from 1 pound up to 13 pounds.
o What weights does
he have?
o What would be
a wise choice of a fourth weight? Up to what weight could he then weigh?
Problems are taken from various sources on the web including:
http://www.puzzles.com/PuzzlePlayground/PuzzlesHome.htm
http://www.math.purdue.edu/pow/
Marion Campus Weekly Problem Contest Spring 1981
Challenging Math Problems Grinnell College 1986-1990