subject
Mathematics, 13.10.2020 05:01 ronaldo22

The Towers of Hanoi puzzle has 3 towers labeled 0,1, and 2. There are n pegs of sizes 1 to n, initially placed on tower 0 from top to bottom in increasing order of their sizes. The goal of the well-known puzzle is to move all n pegs to another tower, say tower 2. One can only move one peg at a time, and move the top peg on a tower to be placed on the top of another tower, and cannot place a larger peg on top of a smaller peg. The question is, what is the smallest number of moves needed. The three towers are still labeled 0, 1, and 2. There is one additional constraint: You are only allowed to move pegs from a tower labeled i to the next one labeled (i+1) mod 3. You can imagine the towers as being arranged in a circular fashion, in which case, the constraint says that you can only move pegs in an anti-clockwise manner. So, for example, in order to move a peg from tower 0 to tower 2, you would have to first move it to tower 1 (if both 0 ā†’ 1 and 1 ā†’ 2 are legal moves at this point), and this sequence would cost two moves instead of just one

Required:
a. Prove that starting at any legal configuration, there is at least one legal move.
b. Inductively prove that for any nā‰„1, this variant of the Towers of Hanoi puzzle (the goal is still moving all n pegs from tower 0 to tower 2) has a solution (consisting of finitely many legal moves.)
c. Give a recurrence of T(n), the least number of moves needed for this variant of the Towers of Hanoi puzzle with n pegs.

ansver
Answers: 1

Another question on Mathematics

question
Mathematics, 21.06.2019 19:00
How do the definitions, properties, and postulates you've learned about line segments, parallel lines, and angles to define the shapes of polygons
Answers: 1
question
Mathematics, 21.06.2019 23:40
Which of the following is best modeled using a linear equation y=ax+b, where a is less than 0?
Answers: 2
question
Mathematics, 22.06.2019 00:30
If m_b=mzd= 43, find mzc so that quadrilateral abcd is a parallelogram o 86 137 o 129 43 description
Answers: 1
question
Mathematics, 22.06.2019 01:10
What is the angle measure, or angle of depression, between this bird and the bird watcher?
Answers: 1
You know the right answer?
The Towers of Hanoi puzzle has 3 towers labeled 0,1, and 2. There are n pegs of sizes 1 to n, initia...
Questions
question
Geography, 19.12.2020 07:10
question
Mathematics, 19.12.2020 07:10
question
Mathematics, 19.12.2020 07:10
question
Mathematics, 19.12.2020 07:10
question
Mathematics, 19.12.2020 07:10
question
Biology, 19.12.2020 07:10
question
Business, 19.12.2020 07:10
question
History, 19.12.2020 07:10
question
World Languages, 19.12.2020 07:10