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An average table (Posted on 2005-06-03) Difficulty: 4 of 5
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.

No Solution Yet Submitted by ronen    
Rating: 4.2500 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Solution | Comment 3 of 10 |
(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

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