Answer Exercise 11 for a 4 × 4 chessboard. [Replace each "nine" in part (b) with "sixteen."]
(a) In how many ways can we paint the cells of a 3 × 3 chessboard using red and blue paint? (The back of the chessboard is black.)
(b) In how many ways can we construct a 3 × 3 chessboard by joining (with paste) the edges of nine 1 × 1 plastic squares that are transparent and tinted red or blue? (There are nine squares of each color available.)