Answer
a) Yes
b)$2^{2n}-1$
c)Polya’s fourth phase.
Work Step by Step
a. Yes. Place the first tile in the center so that it avoids the quadrant
containing the hole while covering one square from each of the other
quadrants. Each quadrant then represents a smaller version of the original
problem.
b. The board with a single hole contains $2^{2n} - 1$ squares, and each tile covers
exactly three squares.
c. Parts (a) and (b) of this question provide an excellent example of how
knowing a solution to one problem helps solve another. See Polya’s
fourth phase.
