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Towers of Hanoi

Towers of Hanoi. Catherine Hornback, UMBC Dr. Leiss Midterm Report, 11 June 2012 Summer 2012 University of Houston REU. Table of Contents. Background Interest of the game Variations Type One Type Two The project. Background. Mathematical puzzle Created by Édouard Lucas in 1883

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Towers of Hanoi

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  1. Towers of Hanoi Catherine Hornback, UMBC Dr. Leiss Midterm Report, 11 June 2012 Summer 2012 University of Houston REU

  2. Table of Contents • Background • Interest of the game • Variations • Type One • Type Two • The project

  3. Background • Mathematical puzzle • Created by ÉdouardLucas in 1883 • Move tower of disks from one peg to another • Divine Rule: No disk may be placed on top of a smaller disk • Can also be played on graphs

  4. Interest of the game • Finding bounds on number of moves • Upper bounds are simpler to find • Lower bounds are much more difficult

  5. Variations • More than three pegs • Circular or cycle graph • Parallel moves • Two versions S D S More than three pegs D Circular game

  6. Type One

  7. Type Two

  8. The project • Illustrate differences between sequential and parallel models • Finding strategies to parallelize moves • Finding the worst possible graphs for both models of parallel moves • Worst is defined as having the largest number of parallel moves • Three and more pegs and any number of disks

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