In the Tower of Hanoi puzzle, suppose our goal is to transfer all n disks from peg 1 to peg 3, but we cannot move a disk directly between pegs 1 and 3. Each move of a disk must be a move involving peg 2. As usual, we cannot place a disk on top of a smaller disk.
a) Find a recurrence relation for the number of moves required to solve the puzzle for n disks with this added restriction.
b) Solve this recurrence relation to find a formula for the number of moves required to solve the puzzle for n disks.
c) How many different arrangements are there of the n disks on three pegs so that no disk is on top of a smaller disk?
d) Show that every allowable arrangement of the n disks occurs in the solution of this variation of the puzzle.
Want to see the full answer?
Check out a sample textbook solutionChapter 8 Solutions
DISCRETE MATHEMATICS LOOSELEAF
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning