You come upon a beautiful waterfall, and look down in hope of something glittering but in vain. However, there is a small path made along the banks of the stream. You wonder when this island was last visited? Initial searches showed it to be uninhabited, but maybe there are people in hiding? You take that path, wary of your surroundings. But what you come across is not a living being, but an ancient relic. A giant chessboard with a weird number etched into one square ... it's Soham's turn to present you with a problem

Consider an $8\times 8$ chessboard, with a complex number written on each of the squares. These numbers are arranged in such a way that the number on each square is the average of the numbers in its surrounding squares. However, Soham only shows you the square f4 which contains the entry $3+2i$. With a bright smile, he asks you how many possible configurations of numbers on the squares are there for this chessboard.

Answer Soham's question. If you are confused about which square has been referred to, take a look at this article on chess notation.