Card_Trick_Problem_Set_Solutions

# Card_Trick_Problem_Set_Solutions -...

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\documentclass[12pt]{article} \title{Card Trick Problem Set Solutions} \usepackage{fullpage} \usepackage[dvips]{graphicx} \author{Michael Allen} \ \begin{document} \maketitle \ \section*{1-4 Lower Bounds} \ With the given procedure, we can establish a lower bound for the size of the deck for which we can perform the card trick for a given number of cards. These results are shown below. g $$\begin{array}{c|c} hand& deck \\\hline 2 & 3 \\ 3 & 6 \\ 4 & 15 \\ 5 & 52 \\ 6 & 245 \\ n & 2(n-1)! + (n-1) \end{array}$$ \section*{5-6 Upper Bounds} \ Our procedure, however, is not optimal, and it is theoretically possible to perform the trick with a larger deck. We can set our upper bound at a size which makes maximal use of the information available to us. a $$\begin{array}{c|c} hand& deck \\\hline 2 & 3 \\ 3 & 8 \\ 4 & 24 \\ 5 & 124 \\ 6 & 725 \\ n & n! + (n-1) \end{array}$$ \newpage \section*{7} \ For the following, assume we have a deck of $d$ cards from which the accomplice chooses a hand of size $n$.

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## This document was uploaded on 10/01/2011.

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Card_Trick_Problem_Set_Solutions -...

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