Problem_Set_03

# Problem_Set_03 -...

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\documentclass{article} \usepackage{hyperref} \def\R2Lurl#1#2{\mbox{\href{#1}{\tt #2}}} \newcommand{\tab}{\makebox[4em]{}} \ \begin{document} \ \begin{center} \textbf{ArsDigita University} \ \end{center} \ \begin{center} \textbf{Month 2: Discrete Mathematics - Professor Shai Simonson} \ \end{center} \ \begin{center} \textbf{Problem Set 3 -- Recursion and Induction} \ \end{center} \ 1.\tab Solve the Chinese Rings Puzzle, also called the Patience Puzzle, (\R2Lurl{http://johnrausch.com/PuzzleWorld/patience.htm } {http://johnrausch.com/PuzzleWorld/patience.htm}). This will prepare you for recursion, recurrence equations, proofs by induction and graph representations. b 2.\tab Consider the variation of the Towers of Hanoi Problem where you have four pegs instead of three. Sloppy Joe designs this \textit{solution:} h

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h In order to move \textit{n} disks from \textit{From} to \textit{To}, using \textit{Using1} and \textit{Using2}: \ If \textit{n} equals 1, then move a disk from \textit{From} to \textit{To,} otherwise do the three recursive steps: d Move \textit{n/2} disks from \textit{From} to \textit{Using1}, using \textit{To} and \textit{Using2;} a Move \textit{n/2} disks from \textit{From} to \textit{To}, using \textit{Using2} and \textit{Using1;}\\ Move \textit{n/2} disks from \textit{Using1} to \textit{To}, using \textit{From} and \textit{Using2;}\\ a.\tab Explain why Sloppy Joe's solution does not work.\\ b.\tab Fruity Freddie suggests changing the second line: b
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Problem_Set_03 -...

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