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\newcommand{\titre}{Les chiffres pivotants}
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\begin{document}

\begin{center}
    \small Un plateau de cases numérotées de 1 à 9 possède 4 boutons (A, B, C, D). Appuyer sur un bouton fait tourner d'un quart de tour, dans le sens des aiguilles d'une montre, les quatre nombres qui l'entourent.
\end{center}
\vspace{0.5em}

Mu a téléchargé un nouveau jeu sur sa tablette, constitué de cases numérotées de 1 à 9 et de 4 boutons (\fcolorbox{black}{yellow}{\textbf{A}}, \fcolorbox{black}{yellow}{\textbf{B}}, \fcolorbox{black}{yellow}{\textbf{C}} et \fcolorbox{black}{yellow}{\textbf{D}}) . Lorsque Mu appuie sur un bouton, les nombres situés autour de ce bouton tournent dans le sens des aiguilles d'une montre.\par

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\medskip
{\large\bfseries\color{red} Niveau 0 . Débutant.}\par\smallskip

Que se passe-t-il si Mu appuie sur le bouton \fcolorbox{black}{yellow}{\textbf{C}} ? (En partant de la position initiale.) Dessiner (schématiquement) le plateau.\par

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\medskip
{\large\bfseries\color{red} Niveau 1 . Renardeau.}\par\smallskip

Sur quel bouton a-t-on appuyé pour obtenir le tableau ci-dessous (En partant de la position initiale)?\par

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  \node[black, anchor=base, font=\fontsize{12.6}{15.1}\selectfont] at (1.541,0.947) {C};
  \node[black, anchor=base, font=\fontsize{11.5}{13.8}\selectfont] at (2.417,0.993) {D};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (1.074,2.442) {4};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (2.000,2.432) {1};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (2.898,2.432) {3};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (1.065,1.497) {5};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (1.981,1.533) {2};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (2.935,1.515) {6};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (1.138,0.580) {7};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (2.036,0.617) {8};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (2.971,0.617) {9};
\end{tikzpicture}\end{center}


\medskip
{\large\bfseries\color{red} Niveau 2 . Louveteau.}\par\smallskip

Que se passe-t-il si Mu appuie sur le bouton \fcolorbox{black}{yellow}{\textbf{D}}, puis sur le bouton \fcolorbox{black}{yellow}{\textbf{A}} (En partant de la position initiale) ?\par

\begin{center}\begin{tikzpicture}[line width=0.6pt]
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  \node[black, anchor=base, font=\fontsize{12.6}{15.1}\selectfont] at (1.541,0.947) {C};
  \node[black, anchor=base, font=\fontsize{11.5}{13.8}\selectfont] at (2.417,0.993) {D};
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  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (2.000,2.432) {2};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (2.898,2.432) {3};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (1.065,1.497) {4};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (1.981,1.533) {5};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (2.935,1.515) {6};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (1.138,0.580) {7};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (2.036,0.617) {8};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (2.971,0.617) {9};
\end{tikzpicture}\end{center}


\begin{center}\begin{tikzpicture}[line width=0.6pt]
  \path[fill=red, fill opacity=0.5] (0.707,2.901) rectangle (1.495,2.112);
  \draw[black] (0.707,2.901) rectangle (1.495,2.112);
  \path[fill=red, fill opacity=0.5] (1.605,2.910) rectangle (2.394,2.121);
  \draw[black] (1.605,2.910) rectangle (2.394,2.121);
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  \draw[black] (2.522,2.928) rectangle (3.310,2.140);
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  \draw[black] (0.735,1.063) rectangle (1.523,0.274);
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  \draw[black] (1.633,1.072) rectangle (2.421,0.284);
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  \draw[black] (2.550,1.090) rectangle (3.338,0.302);
  \path[fill=yellow] (1.349,2.222) rectangle (1.697,1.874);
  \draw[black] (1.349,2.222) rectangle (1.697,1.874);
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  \draw[black] (2.302,2.195) rectangle (2.650,1.846);
  \path[fill=yellow] (1.367,1.260) rectangle (1.715,0.911);
  \draw[black] (1.367,1.260) rectangle (1.715,0.911);
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  \draw[black] (2.247,1.296) rectangle (2.595,0.948);
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  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (1.074,2.442) {?};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (2.000,2.432) {?};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (2.898,2.432) {?};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (1.065,1.497) {?};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (1.981,1.533) {?};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (2.935,1.515) {?};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (1.138,0.580) {?};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (2.036,0.617) {?};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (2.971,0.617) {?};
\end{tikzpicture}\end{center}


\medskip
{\large\bfseries\color{red} Niveau 3 . Panthère noire.}\par\smallskip

Mu a appuyé successivement sur deux boutons pour atteindre la position suivante. Lesquels ?\par

\begin{center}\begin{tikzpicture}[line width=0.6pt]
  \path[fill=red, fill opacity=0.5] (0.707,2.901) rectangle (1.495,2.112);
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  \draw[black] (1.605,2.910) rectangle (2.394,2.121);
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  \draw[black] (2.522,2.928) rectangle (3.310,2.140);
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  \draw[black] (0.716,1.979) rectangle (1.505,1.191);
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  \draw[black] (1.615,1.989) rectangle (2.403,1.200);
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  \draw[black] (2.531,2.007) rectangle (3.320,1.219);
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  \draw[black] (0.735,1.063) rectangle (1.523,0.274);
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  \draw[black] (1.633,1.072) rectangle (2.421,0.284);
  \path[fill=red, fill opacity=0.5] (2.550,1.090) rectangle (3.338,0.302);
  \draw[black] (2.550,1.090) rectangle (3.338,0.302);
  \path[fill=yellow] (1.349,2.222) rectangle (1.697,1.874);
  \draw[black] (1.349,2.222) rectangle (1.697,1.874);
  \path[fill=yellow] (2.302,2.195) rectangle (2.650,1.846);
  \draw[black] (2.302,2.195) rectangle (2.650,1.846);
  \path[fill=yellow] (1.367,1.260) rectangle (1.715,0.911);
  \draw[black] (1.367,1.260) rectangle (1.715,0.911);
  \path[fill=yellow] (2.247,1.296) rectangle (2.595,0.948);
  \draw[black] (2.247,1.296) rectangle (2.595,0.948);
  \node[black, anchor=base, font=\fontsize{9.9}{11.9}\selectfont] at (1.529,1.939) {A};
  \node[black, anchor=base, font=\fontsize{10.8}{13.0}\selectfont] at (2.473,1.912) {B};
  \node[black, anchor=base, font=\fontsize{12.6}{15.1}\selectfont] at (1.541,0.947) {C};
  \node[black, anchor=base, font=\fontsize{11.5}{13.8}\selectfont] at (2.417,0.993) {D};
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  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (2.000,2.432) {2};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (2.898,2.432) {3};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (1.065,1.497) {4};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (1.981,1.533) {5};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (2.935,1.515) {6};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (1.138,0.580) {7};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (2.036,0.617) {8};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (2.971,0.617) {9};
\end{tikzpicture}\end{center}


\begin{center}\begin{tikzpicture}[line width=0.6pt]
  \path[fill=red, fill opacity=0.5] (0.707,2.901) rectangle (1.495,2.112);
  \draw[black] (0.707,2.901) rectangle (1.495,2.112);
  \path[fill=red, fill opacity=0.5] (1.605,2.910) rectangle (2.394,2.121);
  \draw[black] (1.605,2.910) rectangle (2.394,2.121);
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  \draw[black] (2.522,2.928) rectangle (3.310,2.140);
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  \draw[black] (0.716,1.979) rectangle (1.505,1.191);
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  \draw[black] (1.633,1.072) rectangle (2.421,0.284);
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  \draw[black] (2.550,1.090) rectangle (3.338,0.302);
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  \draw[black] (1.349,2.222) rectangle (1.697,1.874);
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  \draw[black] (2.302,2.195) rectangle (2.650,1.846);
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  \draw[black] (1.367,1.260) rectangle (1.715,0.911);
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  \draw[black] (2.247,1.296) rectangle (2.595,0.948);
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  \node[black, anchor=base, font=\fontsize{11.5}{13.8}\selectfont] at (2.417,0.993) {D};
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  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (2.898,2.432) {2};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (1.065,1.497) {4};
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\medskip
{\large\bfseries\color{red} Niveau 4 .Eléphanteau.}\par\smallskip

Mu a appuyé successivement sur les boutons \fcolorbox{black}{yellow}{\textbf{B}}, \fcolorbox{black}{yellow}{\textbf{D}} et \fcolorbox{black}{yellow}{\textbf{C}}. Quel tableau obtient-on ?\par

\begin{center}\begin{tikzpicture}[line width=0.6pt]
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  \draw[black] (0.735,1.063) rectangle (1.523,0.274);
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  \draw[black] (2.302,2.195) rectangle (2.650,1.846);
  \path[fill=yellow] (1.367,1.260) rectangle (1.715,0.911);
  \draw[black] (1.367,1.260) rectangle (1.715,0.911);
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  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (1.065,1.497) {4};
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  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (2.935,1.515) {6};
  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (1.138,0.580) {7};
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  \node[black, anchor=base, font=\fontsize{10.4}{12.5}\selectfont] at (2.971,0.617) {9};
\end{tikzpicture}\end{center}


\begin{center}\begin{tikzpicture}[line width=0.6pt]
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\medskip
{\large\bfseries\color{red} Niveau 5 . Aigle royal.}\par\smallskip

Mu a appuyé successivement sur trois boutons pour atteindre la position suivante. Lesquels ?\par

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\newpage

{\Large\bfseries\color{red} Correction}\par\medskip

Mu a téléchargé un nouveau jeu sur sa tablette, constitué de cases numérotées de 1 à 9 et de 4 boutons (\fcolorbox{black}{yellow}{\textbf{A}}, \fcolorbox{black}{yellow}{\textbf{B}}, \fcolorbox{black}{yellow}{\textbf{C}} et \fcolorbox{black}{yellow}{\textbf{D}}) . Lorsque Mu appuie sur un bouton, les nombres situés autour de ce bouton tournent dans le sens des aiguilles d'une montre.\par

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\medskip
{\large\bfseries\color{red} Niveau 0 . Débutant.}\par\smallskip

Que se passe-t-il si Mu appuie sur le bouton \fcolorbox{black}{yellow}{\textbf{C}} ? (En partant de la position initiale.) Dessiner (schématiquement) le plateau.\par

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\medskip
{\large\bfseries\color{red} Niveau 1 . Renardeau.}\par\smallskip

Sur quel bouton a-t-on appuyé pour obtenir le tableau ci-dessous (En partant de la position initiale)?\par

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Mu a appuyé sur le bouton \fcolorbox{black}{yellow}{\textbf{A}}.\par

\medskip
{\large\bfseries\color{red} Niveau 2 . Louveteau.}\par\smallskip

Que se passe-t-il si Mu appuie sur le bouton \fcolorbox{black}{yellow}{\textbf{D}}, puis sur le bouton \fcolorbox{black}{yellow}{\textbf{A}} (En partant de la position initiale) ?\par

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\medskip
{\large\bfseries\color{red} Niveau 3 . Panthère noire.}\par\smallskip

Mu a appuyé successivement sur deux boutons pour atteindre la position suivante. Lesquels ?\par

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\begin{center}\begin{tikzpicture}[line width=0.6pt]
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Mu a appuyé sur \fcolorbox{black}{yellow}{\textbf{B}} puis sur \fcolorbox{black}{yellow}{\textbf{D}}.Niveau 4 .Eléphanteau. Mu a appuyé successivement sur les boutons \fcolorbox{black}{yellow}{\textbf{B}}, \fcolorbox{black}{yellow}{\textbf{D}} et \fcolorbox{black}{yellow}{\textbf{C}}. Quel tableau obtient-on ?\par

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\begin{center}\begin{tikzpicture}[line width=0.6pt]
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\medskip
{\large\bfseries\color{red} Niveau 5 . Aigle royal.}\par\smallskip

Mu a appuyé successivement sur trois boutons pour atteindre la position suivante. Lesquels ?\par

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\begin{center}\begin{tikzpicture}[line width=0.6pt]
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Mu a appuyé sur \fcolorbox{black}{yellow}{\textbf{D}}, \fcolorbox{black}{yellow}{\textbf{C}} et \fcolorbox{black}{yellow}{\textbf{B}}.\par

\end{document}
