“Imagine an infinite chessboard that contains a positive integer in each square. If the value in each square is equal to the average of its four neighbours to the north, south, west, and east, prove the values in all the squares are equal.”—Zeitz, Paul, The Art and Craft of Problem Solving, Second Edition, p. 82 (problem 3.2.7)

Dr. Zeitz made an assumption which is not necessarily true. If you break with this assumption, you can have the value of a square be the average of its four neighbours to the north, south, west, and east, and yet the values in all the squares are not equal.

What is the assumption? Give at least one example that breaks with the assumption.

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. **The deadline is Wednesday, August 28, 2013 at noon Pacific Time.** I will post the answer shortly after.