Mathematics Problem Of the Week

Fall 2007

POW #1

Coin Grid

Sixteen coins (4 quarters, 4 dimes, 4 nickels and 4 pennies) are arranged on a 4x4 grid like the one shown below. Note that it is easy on this grid to choose one coin from each row so that the total value of the four coins is 41¢ , i.e one coin of each denomination. Is this always possible?

Your task for this POW is either

(a) Find an arrangement of the coins for which it is impossible to get exactly 41¢ by choosing one coin from each row OR

(b) Prove that it is always possible to get 41¢ for any arrangement.

Due Friday, September 7^th at Noon.

Solutions should be submitted to Dr. R. Lock's mailbox in the Math/CS/Stat office or sent via e-mail to rlock@stlawu.edu.