[JEE Advanced 1982] in an m n grid each square holds a number equal to the arithmetic
In an $m\times n$ grid each square holds a number equal to the arithmetic mean of its edge-neighbours. Show this forces all numbers to be equal.
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· 2d ago
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Answer: Proved — all numbers are equal.
The maximum value $M$ appears in some square; being the mean of its neighbours, all its neighbours also equal $M$. Propagating across the connected grid shows every square equals $M$.
JEE Advanced 1982 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.
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