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\documentclass[11pt]{article}
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\usepackage[utf8]{inputenc}
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\usepackage[top=2.0cm, bottom=1.5cm, inner=5.9cm, outer=1.5cm, marginparwidth=3.9cm, marginparsep=0.5cm,footskip=0.5cm]{geometry}
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\usepackage{fancyhdr}
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\usepackage{titlesec}
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\usepackage{titling}
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\reversemarginpar
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\fancyhf{}
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\pagestyle{fancyplain}
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\fancyfoot[R]{\footnotesize vXXX}
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\setlength{\parindent}{0em}
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\setlength{\parskip}{0.2em}
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\titlespacing*{\section}{0pt}{1em}{0.5em}
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\pretitle{\begin{center}\LARGE}
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\posttitle{\par\end{center}}
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\predate{}
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\date{\vspace{-1em}}
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\postdate{}
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\title{How to Solve It}
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\author{George P\'{o}lya}
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\begin{document}
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\maketitle
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\section*{Understanding the Problem}
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\emph{What is the unknown?}
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\marginpar{
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\textbf{First}.
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You have to \emph{understand} the problem.
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}
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\emph{What are the data?}
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\emph{What is the condition?}
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Is it possible to satisfy the condition? Is the condition sufficient to determine the unknown? Or is it insufficient? Or redundant? Or Contradictory?
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Draw a figure.
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Introduce suitable notation.
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Separate the various parts of the condition.
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Can you write them down?
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\section*{Devising a plan}
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Have you seen it before?
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\marginpar{
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\textbf{Second}.
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Find the connection between the data and the unknown.
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You may be obliged to consider auxiliary problems if an immediate connection cannot be found.
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You should obtain eventually a \emph{plan} of the solution.
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}
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Or have you seen the same problem in a slightly different form?
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\emph{Do you know a related problem?}
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Do you know a theorem that could be useful?
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\emph{Look at the unknown!} And try to think of a familiar problem having the same or a similar unknown.
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\emph{Here is a problem related to yours and solved before. Could you use it?}
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Could you use its result?
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Could you use its method?
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Should you introduce some auxiliary element in order to make its use possible?
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Could you restate the problem?
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Could you restate it still differently?
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Go back to definitions.
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If you cannot solve the proposed problem try to solve first some related problem.
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Could you imagine a more accessible related problem?
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A more general problem?
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A more special problem?
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An analogous problem?
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Could you solve a part of the problem?
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Keep only a part of the condition, drop the other part; how far is the unknown then determined, how can it vary?
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Could you derive something useful from the data?
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Could you think of other data appropriate to determine the unknown?
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Could you change the unknown or the data, or both if necessary, so that the new unknown and the new data are nearer to each other?
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Did you use all the data?
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Did you use the whole condition?
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Have you taken into account all essential notions involved in the problem?
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\section*{Carrying out the Plan}
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Carrying out your plan of the solution, \emph{check each step}.
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\marginpar{
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\textbf{Third}.
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\emph{Carry out} yout plan.
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}
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Can you see clearly that the step is correct?
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Can you prove that it is correct?
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\section*{Looking Back}
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Can you \emph{Check the result}?
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\marginpar{
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\textbf{Fourth}.
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\emph{Examine} the solution obtained.
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}
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Can you check the argument?
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Can you derive the result differently?
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Can you see it at a glance?
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Can you use the result, or the method, for some other problem?
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\end{document}

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