(a) Consider an 8 X 8 chessboard. It contains sixty-four 1 × 1 squares and one 8 × 8 square. How many 2 × 2 squares does it contain? How many 3 × 3 squares? How many squares in total?
(b) Now consider an n × n chessboard for some fixed n ∈ Z+. For 1 < k < n, how many k × k squares are contained in this chessboard? How many squares in total?