Given an infinite grid of real numbers between 0 and 100, such that every number in the grid is the average of its four direct neighbours (the numbers to the left, right, above, and below it) prove that all the numbers are necessarily equal, or give a counter-example.

(In reply to re: Solution by Richard)

Another comment: If we had only a finite number of integers, Eric's argument is dead on.

Posted by owl on 2005-06-03 22:13:53