There is a game which has a board which looks just like a chess board, with n rows and n columns, only n is any odd integer greater than 7. Numbers are filled in this board subject to the following rules-
(I) Any number is the negative of the number directly above it, if there is a number directly above it.
(II) Any number is double the number directly to its left if there is a number directly to its left.
If the number is in the upper left corner (first row and first column) is 1, what is the sum of all the numbers in the table?
The point to note here is that although it is mentioned that n>7, the pattern will hold good for all odd values of n.
At n=1, the answer will be 1, which is obtained only at option (c).
Hence, the sum = 2n−1. Answer is option (c).