Math Problems of the Month
OSU-Marion

February 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.



  1. How many rooks can you place on a chess board so that none of them are able to attack any of the others? Can you prove that it is impossible to place more than your number? (Rooks attack any distance vertically or horizontally)


  1. What about if the first problem where knights instead of rooks? (Knights move in an 'L' shape, two spaces in one direction then one space sideways.) Can you find a nice proof that it is impossible to do more than your number?


  1. (Really hard) What about queens...?


  1. Another chessboard problem. Can you cover all of the 64 squares of a chessboard except the two diagonally opposite corners using 31 rectangles? Each rectangle is 2 squares by 1 square.


  1. Suppose you have 4 blue points and 4 red points on a plane so that no three of them are on a line. Is it always possible to find 4 line segments that each connect a different red point to a blue point and no two of the lines cross each other? Show an example where it can't be done or prove it can always be done.




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