A circle, 2n − 1 units in diameter, has been drawn symmetrically on a 2n × 2n chessboard, illustrated here for n = 3: a How many cells of the board contain a segment of the circle? b Find a function...

A circle, 2n − 1 units in diameter, has been drawn symmetrically on a 2n × 2n chessboard, illustrated here for n = 3:

a How many cells of the board contain a segment of the circle?

b Find a function f(n, k) such that exactly

cells of the board lie entirely within the circle.