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\newcommand{\titre}{La tour et ses libert\'es}
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\begin{document}
\newchessgame

\noindent Aux \'echecs, la \textbf{tour} se d\'eplace sur les \textbf{colonnes} (lettres a--h) et les \textbf{rang\'ees} (chiffres 1--8). Par exemple, depuis la case \textbf{d5}, elle peut aller sur les cases surlign\'ees : \texttt{a5, b5, c5, e5, f5, g5, h5, d1, d2, d3, d4, d6, d7, d8}.
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\begin{enumerate}[label=\textbf{\arabic*.},leftmargin=*,itemsep=1.4ex]
  \item \textbf{Une tour en b3.} On retire la tour et on en pose une en \textbf{b3}. Sur quelles cases peut-elle aller ? Combien a-t-elle de libert\'es ?
  \item \textbf{Une enqu\^ete.} Une tour peut se rendre en \textbf{f1} et \textbf{h6}. Sur quelle(s) case(s) est-elle situ\'ee ?
  \item \textbf{Les libert\'es selon la case.} \'Etudie, \`a l'aide d'un diagramme colori\'e et l\'egend\'e, le nombre de libert\'es de la tour \emph{en fonction de sa case de d\'epart}. Que remarques-tu ?
\end{enumerate}
\newpage
\section*{Corrig\'e}
\noindent\textbf{1.} La tour en b3 a \textbf{14 libert\'es} : \texttt{a3, c3, d3, e3, f3, g3, h3, b1, b2, b4, b5, b6, b7, b8}.
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\smallskip\noindent\textbf{2.} Une tour qui peut se rendre en \textbf{f1} et \textbf{h6} se trouve sur \textbf{f6} ou \textbf{h1}. Les fl\`eches montrent, depuis chaque tour, les d\'eplacements vers les deux cases de d\'epart.
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\smallskip\noindent\textbf{3.}
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\nopagebreak\begin{center}\footnotesize
\colorbox{red!50!yellow}{~~}~\textbf{14} libert\'es sur \emph{toutes} les cases
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\noindent La tour est un cas \`a part : elle a \textbf{14 libert\'es sur absolument toutes les cases} (7 sur sa rang\'ee + 7 sur sa colonne). Sa libert\'e ne d\'epend \emph{jamais} de sa position --- c'est un \textbf{invariant}.
\end{document}