# Chapter 5 - Algorithms - Section 5.3 - Algorithm Discovery - Questions & Exercises - Page 234: 2

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.

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