# infinite chessboard average!

The $$n^2$$ squares of an $$n \times n$$ chessboard are filled with positive integers in such a way that each integer is the average of the integers on the neighbouring squares (sharing common edge and vertex). Let $$k$$ be the number of all such distinct configurations. What is the value of $$\displaystyle \lim_{n \to \infty} \frac{k}{n}$$?

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