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Question 8. Remember the Towers of Hanoi problem, in which a sequence of disks of decreasing size needs to be moved from a start peg to a goal peg using a middle peg as intermediate storage one disk at a time, and a large disk cannot be placed on top of a smaller disk. We modify the initial problem, so every disk moves only to adjacent pegs (e.g. no jumps between the leftmost peg to the rightmost peg). The recurrence relation for this variation of the problem is: an = 3an-1 +2, ao = 2

Question 8. Remember the Towers of Hanoi problem, in which a sequence of disks of decreasing size needs to be moved from a start peg to a goal peg using a middle peg as intermediate storage one disk at a time, and a large disk cannot be placed on top of a smaller disk. We modify the initial problem, so every disk moves only to adjacent pegs (e.g. no jumps between the leftmost peg to the rightmost peg). The recurrence relation for this variation of the problem is: an = 3an-1 +2, ao = 2

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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Question 8. Remember the Towers of Hanoi problem, in which a sequence of disks of decreasing size needs to be moved from a start peg to a goal peg using a middle peg as intermediate storage one disk at a time, and a large disk cannot be placed on top of a smaller disk. We modify the initial problem, so every disk moves only to adjacent pegs (e.g. no jumps between the leftmost peg to the rightmost peg). The recurrence relation for this variation of the problem is: аn — Зап-1 +2, аg 3D 2 a. Suppose that, instead of one disk of each size, you have three. Find the recurrence relation for this problem and solve it in closed form. b. Suppose a robot can move one disk every 0.01 seconds. What is the largest Tower of Hanoi in terms of number of disks that can be solved under 60 minutes for this new problem?
Transcribed Image Text:Question 8. Remember the Towers of Hanoi problem, in which a sequence of disks of decreasing size needs to be moved from a start peg to a goal peg using a middle peg as intermediate storage one disk at a time, and a large disk cannot be placed on top of a smaller disk. We modify the initial problem, so every disk moves only to adjacent pegs (e.g. no jumps between the leftmost peg to the rightmost peg). The recurrence relation for this variation of the problem is: аn — Зап-1 +2, аg 3D 2 a. Suppose that, instead of one disk of each size, you have three. Find the recurrence relation for this problem and solve it in closed form. b. Suppose a robot can move one disk every 0.01 seconds. What is the largest Tower of Hanoi in terms of number of disks that can be solved under 60 minutes for this new problem?
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