Q. Sixty four squares of a chess board are filled with positive integers one on each in such a way that each integer is the average of the integers on the neighboring squares. (Two squares are neighbours if they share a common edge or vertex. Thus a square can have 8,5 or 3 neighbours depending on its position.) Show that all the sixty four entries are in fact equal.(adsbygoogle = window.adsbygoogle || []).push({});

How does one begin this problem? I initially thought of assuming the contrary(that all the numbers are distinct) and then tried to obtain some ridiculous conclusion. But all I got were equations with innmuerable unknowns! Can anyone please give me a hint on starting the problem? Please DO NOT post the entire solution, as I would like to solve this on my own. Thanks! :D

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# Homework Help: Olympiad problem

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