PLEASE HURRY

Bob discovered that he can bubble any n n square, where n is odd, using a consistent pattern, as shown below for n = 5 and n = 7.

Bobs bubbling of a square partitions the n n square into gray and white areas. For instance, we have a total of 18 areas for the 5 5 square, and a total of 32 areas for the 7 7 square, as shown above.

(a) (2 points) For n being odd, express the total number of areas (both gray and white) in the bubbling of an n n square, as a function of n.

(b) (4 point) Given a 3 3 square, and 9 points arbitrarily placed within the square, prove that two of these points are at a distance of at most 2 from each other. Hint: Bubble the 3 3 square using Bobs pattern.