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\begin{document}
\newchessgame

\noindent Aux \'echecs, la \textbf{dame} est la pi\`ece la plus puissante : elle se d\'eplace comme la \textbf{tour} (lignes et colonnes) \emph{et} comme le \textbf{fou} (diagonales). Par exemple, depuis la case \textbf{d4}, elle peut aller sur les cases surlign\'ees : \texttt{a1, a4, a7, b2, b4, b6, c3, c4, c5, d1, d2, d3, d5, d6, d7, d8, e3, e4, e5, f2, f4, f6, g1, g4, g7, h4, h8}.
\begin{center}
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\begin{enumerate}[label=\textbf{\arabic*.},leftmargin=*,itemsep=1.4ex]
  \item \textbf{Une dame en c2.} On pose une dame en \textbf{c2}. Sur quelles cases peut-elle aller ? Combien a-t-elle de libert\'es ?
  \item \textbf{Une enqu\^ete.} Une dame peut se rendre en \textbf{h2}, \textbf{b4} et \textbf{e7}. 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 dame \emph{en fonction de sa case de d\'epart}. Que remarques-tu ?
\end{enumerate}
\newpage
\section*{Corrig\'e}
\noindent\textbf{1.} La dame en c2 a \textbf{23 libert\'es} : \texttt{a2, a4, b1, b2, b3, c1, c3, c4, c5, c6, c7, c8, d1, d2, d3, e2, e4, f2, f5, g2, g6, h2, h7}.
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\smallskip\noindent\textbf{2.} Une dame qui peut se rendre en \textbf{h2}, \textbf{b4} et \textbf{e7} se trouve sur \textbf{d6} ou \textbf{h4}. Chacune \emph{voit} les trois cases par une ligne, une colonne ou une diagonale (les fl\`eches montrent les trajets).
\begin{center}
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\nopagebreak\begin{center}\footnotesize
\colorbox{yellow!70}{~~}~h2 \quad \colorbox{blue!35}{~~}~b4 \quad \colorbox{red!55}{~~}~e7 \quad \textcolor{green!55!black}{\textbf{\textrightarrow}}~trajets des dames vers les 3 indices
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\smallskip\noindent\textbf{3.}
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\nopagebreak\begin{center}\footnotesize
\colorbox{red!0!yellow}{~~}~21 \quad \colorbox{red!33!yellow}{~~}~23 \quad \colorbox{red!67!yellow}{~~}~25 \quad \colorbox{red!100!yellow}{~~}~27 \quad libert\'es
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\noindent La dame cumule la tour (14 partout) et le fou (7 \`a 13) : ses libert\'es varient de \textbf{21} dans un coin \`a \textbf{27} au centre, en \textbf{anneaux} comme le fou mais toujours \textbf{14 de plus}.
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