\documentclass[a4paper,11pt]{article}

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage[french]{babel}
\usepackage[a4paper,top=3.2cm,bottom=2cm,left=2cm,right=2cm]{geometry}
\usepackage{graphicx}
\usepackage[export]{adjustbox}
\usepackage{fancyhdr}
\usepackage{qrcode}
\usepackage[table]{xcolor}
\usepackage{amsmath,amssymb}
\usepackage{enumitem}
% Puces nettes (babel-french remplace sinon la puce par un tiret « – » peu pro).
% Vaut pour TOUTES les fiches qui importent ce module. AtBeginDocument pour
% passer après la personnalisation des listes faite par babel-french.
\AtBeginDocument{%
  \setlist[itemize]{leftmargin=1.8em,itemsep=0.5ex,topsep=0.4ex,parsep=0pt}%
  \setlist[itemize,1]{label=\textcolor{red!75!black}{\small\textbullet}}%
  \setlist[itemize,2]{label=\textcolor{red!75!black}{\scriptsize\textbullet}}%
}
% Titres compacts (gain de place vertical, fiches plus denses) — vaut pour tous.
\usepackage{titlesec}
\titlespacing*{\section}{0pt}{1.4ex}{0.6ex}
\titlespacing*{\subsection}{0pt}{1.0ex}{0.3ex}
% multicol : listes denses (calcul mental) sur 2 colonnes — neutre tant qu'il
% n'est pas utilisé, dispo pour tous les générateurs.
\usepackage{multicol}
\setlength{\columnsep}{1.5em}
% needspace : empêche un titre d'exercice de rester orphelin en bas de page
% (réserve quelques lignes ; sinon le titre passe à la page suivante avec sa
% liste). Neutre tant qu'il n'est pas appelé — dispo pour tous les générateurs.
\usepackage{needspace}
\usepackage{tikz}
\usetikzlibrary{decorations.text}

\usepackage{tgheros}
\pagestyle{fancy}
\fancyhf{}
\setlength{\headheight}{75pt}
\setlength{\headsep}{10pt}

\newcommand{\logowouf}{%
\begin{tikzpicture}[baseline={(current bounding box.center)},scale=0.55,
                    line cap=round,line join=round]
    \path[use as bounding box] (-2.20,-1.45) rectangle (2.20,2.20);
    \path[
        postaction={decorate},
        decoration={
            text along path,
            text={|\fontfamily{qhv}\bfseries\fontsize{9}{9}\selectfont|site2wouf.fr},
            text align={center},
            raise=0.03ex
        }
    ] (-1.29,0.48) arc[start angle=160,end angle=20,radius=1.29];
    \begin{scope}[xshift=-0.06cm]
        \fill[black] (-0.66,0.14) ellipse (0.21 and 0.31);
        \fill[black] ( 0.66,0.14) ellipse (0.21 and 0.31);
        \fill[black] (-0.23,0.49) ellipse (0.22 and 0.35);
        \fill[black] ( 0.23,0.49) ellipse (0.22 and 0.35);
        \fill[black]
            (0,-0.10)
            .. controls (-0.36,-0.02) and (-0.63,-0.24) .. (-0.58,-0.58)
            .. controls (-0.52,-0.93) and (-0.16,-1.12) .. (0,-0.90)
            .. controls (0.16,-1.12) and (0.52,-0.93) .. (0.58,-0.58)
            .. controls (0.63,-0.24) and (0.36,-0.02) .. (0,-0.10)
            -- cycle;
    \end{scope}
\end{tikzpicture}%
}
\DeclareUnicodeCharacter{2460}{\textcircled{\scriptsize 1}}
\DeclareUnicodeCharacter{2461}{\textcircled{\scriptsize 2}}
\DeclareUnicodeCharacter{2462}{\textcircled{\scriptsize 3}}
\DeclareUnicodeCharacter{2463}{\textcircled{\scriptsize 4}}
\DeclareUnicodeCharacter{2464}{\textcircled{\scriptsize 5}}
\DeclareUnicodeCharacter{2465}{\textcircled{\scriptsize 6}}
\DeclareUnicodeCharacter{2466}{\textcircled{\scriptsize 7}}
\DeclareUnicodeCharacter{2467}{\textcircled{\scriptsize 8}}
\DeclareUnicodeCharacter{2468}{\textcircled{\scriptsize 9}}
\DeclareUnicodeCharacter{2469}{\textcircled{\scriptsize 10}}
\DeclareUnicodeCharacter{246A}{\textcircled{\scriptsize 11}}
\DeclareUnicodeCharacter{246B}{\textcircled{\scriptsize 12}}
\DeclareUnicodeCharacter{246C}{\textcircled{\scriptsize 13}}
\DeclareUnicodeCharacter{246D}{\textcircled{\scriptsize 14}}
\DeclareUnicodeCharacter{246E}{\textcircled{\scriptsize 15}}
\DeclareUnicodeCharacter{246F}{\textcircled{\scriptsize 16}}
\DeclareUnicodeCharacter{2470}{\textcircled{\scriptsize 17}}
\DeclareUnicodeCharacter{2471}{\textcircled{\scriptsize 18}}
\DeclareUnicodeCharacter{2472}{\textcircled{\scriptsize 19}}
\DeclareUnicodeCharacter{2473}{\textcircled{\scriptsize 20}}
\DeclareUnicodeCharacter{24B6}{\textcircled{\scriptsize A}}
\DeclareUnicodeCharacter{24B7}{\textcircled{\scriptsize B}}
\DeclareUnicodeCharacter{24B8}{\textcircled{\scriptsize C}}
\DeclareUnicodeCharacter{24B9}{\textcircled{\scriptsize D}}
\DeclareUnicodeCharacter{24BA}{\textcircled{\scriptsize E}}
\DeclareUnicodeCharacter{24BB}{\textcircled{\scriptsize F}}
\DeclareUnicodeCharacter{24BC}{\textcircled{\scriptsize G}}
\DeclareUnicodeCharacter{24BD}{\textcircled{\scriptsize H}}
\DeclareUnicodeCharacter{24BE}{\textcircled{\scriptsize I}}
\DeclareUnicodeCharacter{24BF}{\textcircled{\scriptsize J}}
\DeclareUnicodeCharacter{24C0}{\textcircled{\scriptsize K}}
\DeclareUnicodeCharacter{24C1}{\textcircled{\scriptsize L}}
\DeclareUnicodeCharacter{24C2}{\textcircled{\scriptsize M}}
\DeclareUnicodeCharacter{24C3}{\textcircled{\scriptsize N}}
\DeclareUnicodeCharacter{24C4}{\textcircled{\scriptsize O}}
\DeclareUnicodeCharacter{24C5}{\textcircled{\scriptsize P}}
\DeclareUnicodeCharacter{24C6}{\textcircled{\scriptsize Q}}
\DeclareUnicodeCharacter{24C7}{\textcircled{\scriptsize R}}
\DeclareUnicodeCharacter{24C8}{\textcircled{\scriptsize S}}
\DeclareUnicodeCharacter{24C9}{\textcircled{\scriptsize T}}
\DeclareUnicodeCharacter{24CA}{\textcircled{\scriptsize U}}
\DeclareUnicodeCharacter{24CB}{\textcircled{\scriptsize V}}
\DeclareUnicodeCharacter{24CC}{\textcircled{\scriptsize W}}
\DeclareUnicodeCharacter{24CD}{\textcircled{\scriptsize X}}
\DeclareUnicodeCharacter{24CE}{\textcircled{\scriptsize Y}}
\DeclareUnicodeCharacter{24CF}{\textcircled{\scriptsize Z}}
\DeclareUnicodeCharacter{24D0}{\textcircled{\scriptsize a}}
\DeclareUnicodeCharacter{24D1}{\textcircled{\scriptsize b}}
\DeclareUnicodeCharacter{24D2}{\textcircled{\scriptsize c}}
\DeclareUnicodeCharacter{24D3}{\textcircled{\scriptsize d}}
\DeclareUnicodeCharacter{24D4}{\textcircled{\scriptsize e}}
\DeclareUnicodeCharacter{24D5}{\textcircled{\scriptsize f}}
\DeclareUnicodeCharacter{24D6}{\textcircled{\scriptsize g}}
\DeclareUnicodeCharacter{24D7}{\textcircled{\scriptsize h}}
\DeclareUnicodeCharacter{24D8}{\textcircled{\scriptsize i}}
\DeclareUnicodeCharacter{24D9}{\textcircled{\scriptsize j}}

\newcommand{\titre}{Le car de ramassage}
\newcommand{\soustitre}{Probl\`eme --- Fiche n\textdegree 42}

\fancyhead[C]{%
\raisebox{4pt}{%
\begin{minipage}[c]{0.15\textwidth}
    \centering
    \logowouf
\end{minipage}
\begin{minipage}[c]{0.62\textwidth}
    \centering
    {\Large\bfseries \titre\par}
    {\small\color{gray} \soustitre}
\end{minipage}
\begin{minipage}[c]{0.21\textwidth}
    \centering
    \qrcode[height=1.5cm]{https://site2wouf.fr/car_de_ramassage.php?x=42}\\[2pt]
    {\small\ttfamily\bfseries\color{red} HAMI0042}
\end{minipage}%
}
}

\begin{document}

\begin{center}
    \small Un car de ramassage doit s'arrêter à chaque carrefour d'un quartier, une fois et une seule. Selon le plan c'est possible ou non — et un simple coloriage permet souvent de le dire d'avance, sans essayer.
\end{center}
\vspace{0.5em}
\sloppy
\needspace{5\baselineskip}
\subsection*{\textcolor{red}{Le car de ramassage}}
\needspace{3\baselineskip}
\begin{center}
\begin{tikzpicture}[scale=0.6076, line join=round, line cap=round]
\draw[line width=0.5pt] (11.292,11.555) -- (11.231,11.293) -- (11.175,11.03) -- (11.126,10.766) -- (11.083,10.501) -- (11.046,10.234) -- (11.015,9.967) -- (10.991,9.699) -- (10.973,9.431) -- (10.961,9.162) -- (10.956,8.893) -- (10.957,8.625) -- (10.964,8.356) -- (10.978,8.088) -- (10.998,7.82);
\draw[line width=0.5pt] (4.103,8.726) -- (4.391,8.749) -- (4.679,8.766) -- (4.968,8.776) -- (5.257,8.778) -- (5.546,8.775) -- (5.835,8.764) -- (6.123,8.747) -- (6.411,8.722) -- (6.698,8.691) -- (6.985,8.654) -- (7.27,8.609) -- (7.555,8.558) -- (7.838,8.5) -- (8.119,8.436);
\draw[line width=0.5pt] (4.103,8.726) -- (4.077,8.496) -- (4.055,8.266) -- (4.04,8.036) -- (4.029,7.805) -- (4.024,7.574) -- (4.025,7.342) -- (4.031,7.111) -- (4.042,6.88) -- (4.059,6.65) -- (4.081,6.419) -- (4.109,6.19) -- (4.142,5.961) -- (4.18,5.733) -- (4.224,5.507);
\draw[line width=0.5pt] (8.119,8.436) -- (8.33,8.424) -- (8.54,8.407) -- (8.75,8.384) -- (8.96,8.357) -- (9.169,8.325) -- (9.377,8.288) -- (9.584,8.247) -- (9.79,8.2) -- (9.995,8.148) -- (10.198,8.092) -- (10.401,8.031) -- (10.601,7.965) -- (10.8,7.895) -- (10.998,7.82);
\draw[line width=0.5pt] (8.119,8.436) -- (8.047,8.181) -- (7.981,7.924) -- (7.921,7.666) -- (7.867,7.406) -- (7.819,7.145) -- (7.777,6.883) -- (7.742,6.62) -- (7.712,6.356) -- (7.689,6.092) -- (7.672,5.827) -- (7.661,5.562) -- (7.657,5.296) -- (7.659,5.031) -- (7.667,4.766);
\draw[line width=0.5pt] (1.414,8.267) -- (1.599,8.329) -- (1.787,8.387) -- (1.975,8.44) -- (2.165,8.489) -- (2.355,8.533) -- (2.547,8.572) -- (2.74,8.608) -- (2.933,8.638) -- (3.127,8.664) -- (3.322,8.686) -- (3.517,8.703) -- (3.712,8.715) -- (3.908,8.723) -- (4.103,8.726);
\draw[line width=0.5pt] (1.414,8.267) -- (1.37,8.004) -- (1.333,7.74) -- (1.302,7.475) -- (1.277,7.209) -- (1.259,6.943) -- (1.247,6.676) -- (1.241,6.409) -- (1.241,6.142) -- (1.248,5.875) -- (1.261,5.608) -- (1.28,5.342) -- (1.305,5.076) -- (1.337,4.811) -- (1.375,4.547);
\draw[line width=0.5pt] (10.998,7.82) -- (11.044,7.619) -- (11.085,7.417) -- (11.121,7.215) -- (11.153,7.011) -- (11.18,6.807) -- (11.202,6.602) -- (11.219,6.396) -- (11.231,6.191) -- (11.239,5.985) -- (11.241,5.779) -- (11.239,5.573) -- (11.232,5.367) -- (11.22,5.161) -- (11.204,4.956);
\draw[line width=0.5pt] (4.224,5.507) -- (4.46,5.416) -- (4.698,5.332) -- (4.938,5.253) -- (5.18,5.18) -- (5.423,5.112) -- (5.669,5.05) -- (5.915,4.994) -- (6.163,4.944) -- (6.412,4.9) -- (6.661,4.861) -- (6.912,4.828) -- (7.163,4.802) -- (7.415,4.781) -- (7.667,4.766);
\draw[line width=0.5pt] (4.224,5.507) -- (4.296,5.233) -- (4.362,4.959) -- (4.421,4.682) -- (4.473,4.404) -- (4.519,4.125) -- (4.558,3.845) -- (4.591,3.564) -- (4.617,3.283) -- (4.637,3.001) -- (4.65,2.718) -- (4.656,2.436) -- (4.656,2.153) -- (4.649,1.871) -- (4.635,1.588);
\draw[line width=0.5pt] (11.204,4.956) -- (11.15,4.742) -- (11.101,4.527) -- (11.058,4.311) -- (11.019,4.094) -- (10.986,3.876) -- (10.957,3.657) -- (10.934,3.438) -- (10.916,3.218) -- (10.903,2.998) -- (10.896,2.777) -- (10.893,2.557) -- (10.896,2.336) -- (10.904,2.116) -- (10.917,1.896);
\draw[line width=0.5pt] (7.667,4.766) -- (7.916,4.818) -- (8.165,4.865) -- (8.416,4.905) -- (8.668,4.939) -- (8.921,4.968) -- (9.174,4.99) -- (9.428,5.007) -- (9.682,5.018) -- (9.936,5.022) -- (10.19,5.021) -- (10.444,5.014) -- (10.698,5.001) -- (10.951,4.981) -- (11.204,4.956);
\draw[line width=0.5pt] (7.667,4.766) -- (7.616,4.541) -- (7.57,4.315) -- (7.529,4.088) -- (7.493,3.859) -- (7.463,3.63) -- (7.439,3.4) -- (7.42,3.17) -- (7.406,2.939) -- (7.398,2.708) -- (7.395,2.477) -- (7.397,2.246) -- (7.405,2.015) -- (7.418,1.785) -- (7.437,1.555);
\draw[line width=0.5pt] (1.375,4.547) -- (1.566,4.646) -- (1.76,4.741) -- (1.956,4.831) -- (2.154,4.917) -- (2.354,4.997) -- (2.556,5.073) -- (2.76,5.145) -- (2.965,5.211) -- (3.172,5.273) -- (3.38,5.329) -- (3.59,5.381) -- (3.8,5.428) -- (4.012,5.47) -- (4.224,5.507);
\draw[line width=0.5pt] (1.375,4.547) -- (1.369,4.357) -- (1.368,4.167) -- (1.372,3.976) -- (1.38,3.786) -- (1.393,3.596) -- (1.41,3.407) -- (1.431,3.217) -- (1.457,3.029) -- (1.488,2.841) -- (1.522,2.653) -- (1.561,2.467) -- (1.605,2.282) -- (1.653,2.097) -- (1.705,1.915);
\draw[line width=0.5pt] (1.705,1.915) -- (1.916,1.923) -- (2.128,1.927) -- (2.339,1.926) -- (2.551,1.92) -- (2.762,1.909) -- (2.973,1.893) -- (3.183,1.872) -- (3.394,1.846) -- (3.603,1.816) -- (3.811,1.78) -- (4.019,1.739) -- (4.226,1.694) -- (4.431,1.644) -- (4.635,1.588);
\draw[line width=0.5pt] (4.635,1.588) -- (4.833,1.555) -- (5.032,1.527) -- (5.232,1.503) -- (5.432,1.484) -- (5.633,1.47) -- (5.834,1.461) -- (6.035,1.456) -- (6.236,1.456) -- (6.437,1.461) -- (6.638,1.47) -- (6.839,1.484) -- (7.039,1.503) -- (7.238,1.526) -- (7.437,1.555);
\draw[line width=0.5pt] (7.437,1.555) -- (7.68,1.617) -- (7.924,1.673) -- (8.17,1.724) -- (8.417,1.769) -- (8.665,1.808) -- (8.914,1.841) -- (9.163,1.869) -- (9.413,1.89) -- (9.664,1.906) -- (9.914,1.916) -- (10.165,1.92) -- (10.416,1.918) -- (10.667,1.91) -- (10.917,1.896);
\filldraw[fill=red!16, draw=black, line width=0.5pt] (11.452,11.555) -- (11.431,11.635) -- (11.372,11.693) -- (11.292,11.715) -- (11.212,11.693) -- (11.154,11.635) -- (11.132,11.555) -- (11.154,11.475) -- (11.212,11.416) -- (11.292,11.395) -- (11.372,11.416) -- (11.431,11.475) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (4.263,8.726) -- (4.242,8.806) -- (4.183,8.864) -- (4.103,8.886) -- (4.023,8.864) -- (3.965,8.806) -- (3.943,8.726) -- (3.965,8.646) -- (4.023,8.587) -- (4.103,8.566) -- (4.183,8.587) -- (4.242,8.646) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (8.279,8.436) -- (8.258,8.516) -- (8.199,8.575) -- (8.119,8.596) -- (8.039,8.575) -- (7.98,8.516) -- (7.959,8.436) -- (7.98,8.356) -- (8.039,8.297) -- (8.119,8.276) -- (8.199,8.297) -- (8.258,8.356) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (1.574,8.267) -- (1.553,8.347) -- (1.494,8.406) -- (1.414,8.427) -- (1.334,8.406) -- (1.275,8.347) -- (1.254,8.267) -- (1.275,8.187) -- (1.334,8.129) -- (1.414,8.107) -- (1.494,8.129) -- (1.553,8.187) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (11.158,7.82) -- (11.136,7.9) -- (11.078,7.958) -- (10.998,7.98) -- (10.918,7.958) -- (10.859,7.9) -- (10.838,7.82) -- (10.859,7.74) -- (10.918,7.681) -- (10.998,7.66) -- (11.078,7.681) -- (11.136,7.74) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (4.384,5.507) -- (4.363,5.587) -- (4.304,5.645) -- (4.224,5.667) -- (4.144,5.645) -- (4.086,5.587) -- (4.064,5.507) -- (4.086,5.427) -- (4.144,5.368) -- (4.224,5.347) -- (4.304,5.368) -- (4.363,5.427) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (11.364,4.956) -- (11.342,5.036) -- (11.284,5.095) -- (11.204,5.116) -- (11.124,5.095) -- (11.065,5.036) -- (11.044,4.956) -- (11.065,4.876) -- (11.124,4.818) -- (11.204,4.796) -- (11.284,4.818) -- (11.342,4.876) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (7.827,4.766) -- (7.806,4.846) -- (7.747,4.905) -- (7.667,4.926) -- (7.587,4.905) -- (7.528,4.846) -- (7.507,4.766) -- (7.528,4.686) -- (7.587,4.628) -- (7.667,4.606) -- (7.747,4.628) -- (7.806,4.686) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (1.535,4.547) -- (1.513,4.627) -- (1.455,4.686) -- (1.375,4.707) -- (1.295,4.686) -- (1.236,4.627) -- (1.215,4.547) -- (1.236,4.467) -- (1.295,4.409) -- (1.375,4.387) -- (1.455,4.409) -- (1.513,4.467) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (1.865,1.915) -- (1.844,1.995) -- (1.785,2.053) -- (1.705,2.075) -- (1.625,2.053) -- (1.566,1.995) -- (1.545,1.915) -- (1.566,1.835) -- (1.625,1.776) -- (1.705,1.755) -- (1.785,1.776) -- (1.844,1.835) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (11.077,1.896) -- (11.056,1.976) -- (10.997,2.034) -- (10.917,2.056) -- (10.837,2.034) -- (10.778,1.976) -- (10.757,1.896) -- (10.778,1.816) -- (10.837,1.757) -- (10.917,1.736) -- (10.997,1.757) -- (11.056,1.816) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (4.795,1.588) -- (4.774,1.668) -- (4.715,1.727) -- (4.635,1.748) -- (4.555,1.727) -- (4.496,1.668) -- (4.475,1.588) -- (4.496,1.508) -- (4.555,1.45) -- (4.635,1.428) -- (4.715,1.45) -- (4.774,1.508) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (7.597,1.555) -- (7.576,1.635) -- (7.517,1.693) -- (7.437,1.715) -- (7.357,1.693) -- (7.299,1.635) -- (7.277,1.555) -- (7.299,1.475) -- (7.357,1.416) -- (7.437,1.395) -- (7.517,1.416) -- (7.576,1.475) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (11.384,9.274) -- (11.505,9.294) -- (11.615,9.35) -- (11.702,9.437) -- (11.758,9.547) -- (11.777,9.668) -- (11.758,9.79) -- (11.702,9.9) -- (11.615,9.987) -- (11.505,10.043) -- (11.384,10.062) -- (11.384,10.062) -- (11.262,10.043) -- (11.152,9.987) -- (11.065,9.9) -- (11.009,9.79) -- (10.99,9.668) -- (11.009,9.547) -- (11.065,9.437) -- (11.152,9.35) -- (11.262,9.294) -- (11.384,9.274) -- cycle;
\node at (11.384,9.668) {\scalebox{1.646}{\small 1}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.151,8.745) -- (6.273,8.765) -- (6.383,8.821) -- (6.47,8.908) -- (6.526,9.018) -- (6.545,9.139) -- (6.526,9.261) -- (6.47,9.371) -- (6.383,9.458) -- (6.273,9.514) -- (6.151,9.533) -- (6.151,9.533) -- (6.03,9.514) -- (5.92,9.458) -- (5.833,9.371) -- (5.777,9.261) -- (5.758,9.139) -- (5.777,9.018) -- (5.833,8.908) -- (5.92,8.821) -- (6.03,8.765) -- (6.151,8.745) -- cycle;
\node at (6.151,9.139) {\scalebox{1.646}{\small 2}};
\filldraw[fill=white, draw=black, line width=0.5pt] (4.425,6.732) -- (4.546,6.751) -- (4.656,6.807) -- (4.743,6.894) -- (4.799,7.004) -- (4.818,7.126) -- (4.799,7.248) -- (4.743,7.358) -- (4.656,7.445) -- (4.546,7.501) -- (4.425,7.52) -- (4.425,7.52) -- (4.303,7.501) -- (4.193,7.445) -- (4.106,7.358) -- (4.05,7.248) -- (4.031,7.126) -- (4.05,7.004) -- (4.106,6.894) -- (4.193,6.807) -- (4.303,6.751) -- (4.425,6.732) -- cycle;
\node at (4.425,7.126) {\scalebox{1.646}{\small 3}};
\filldraw[fill=white, draw=black, line width=0.5pt] (9.666,8.238) -- (9.788,8.257) -- (9.898,8.313) -- (9.985,8.4) -- (10.041,8.51) -- (10.06,8.632) -- (10.041,8.753) -- (9.985,8.863) -- (9.898,8.95) -- (9.788,9.006) -- (9.666,9.026) -- (9.666,9.026) -- (9.544,9.006) -- (9.435,8.95) -- (9.348,8.863) -- (9.292,8.753) -- (9.272,8.632) -- (9.292,8.51) -- (9.348,8.4) -- (9.435,8.313) -- (9.544,8.257) -- (9.666,8.238) -- cycle;
\node at (9.666,8.632) {\scalebox{1.646}{\small 4}};
\filldraw[fill=white, draw=black, line width=0.5pt] (8.133,6.178) -- (8.254,6.197) -- (8.364,6.253) -- (8.451,6.34) -- (8.507,6.45) -- (8.526,6.572) -- (8.507,6.693) -- (8.451,6.803) -- (8.364,6.89) -- (8.254,6.946) -- (8.133,6.965) -- (8.133,6.965) -- (8.011,6.946) -- (7.901,6.89) -- (7.814,6.803) -- (7.758,6.693) -- (7.739,6.572) -- (7.758,6.45) -- (7.814,6.34) -- (7.901,6.253) -- (8.011,6.197) -- (8.133,6.178) -- cycle;
\node at (8.133,6.572) {\scalebox{1.646}{\small 5}};
\filldraw[fill=white, draw=black, line width=0.5pt] (2.674,8.602) -- (2.795,8.621) -- (2.905,8.677) -- (2.992,8.764) -- (3.048,8.874) -- (3.067,8.996) -- (3.048,9.118) -- (2.992,9.227) -- (2.905,9.315) -- (2.795,9.37) -- (2.674,9.39) -- (2.674,9.39) -- (2.552,9.37) -- (2.442,9.315) -- (2.355,9.227) -- (2.299,9.118) -- (2.28,8.996) -- (2.299,8.874) -- (2.355,8.764) -- (2.442,8.677) -- (2.552,8.621) -- (2.674,8.602) -- cycle;
\node at (2.674,8.996) {\scalebox{1.646}{\small 6}};
\filldraw[fill=white, draw=black, line width=0.5pt] (1.635,6.011) -- (1.756,6.03) -- (1.866,6.086) -- (1.953,6.173) -- (2.009,6.283) -- (2.029,6.405) -- (2.009,6.527) -- (1.953,6.636) -- (1.866,6.723) -- (1.756,6.779) -- (1.635,6.799) -- (1.635,6.799) -- (1.513,6.779) -- (1.403,6.723) -- (1.316,6.636) -- (1.26,6.527) -- (1.241,6.405) -- (1.26,6.283) -- (1.316,6.173) -- (1.403,6.086) -- (1.513,6.03) -- (1.635,6.011) -- cycle;
\node at (1.635,6.405) {\scalebox{1.646}{\small 7}};
\filldraw[fill=white, draw=black, line width=0.5pt] (11.612,6.031) -- (11.733,6.05) -- (11.843,6.106) -- (11.93,6.193) -- (11.986,6.303) -- (12.006,6.425) -- (11.986,6.546) -- (11.93,6.656) -- (11.843,6.743) -- (11.733,6.799) -- (11.612,6.819) -- (11.612,6.819) -- (11.49,6.799) -- (11.38,6.743) -- (11.293,6.656) -- (11.237,6.546) -- (11.218,6.425) -- (11.237,6.303) -- (11.293,6.193) -- (11.38,6.106) -- (11.49,6.05) -- (11.612,6.031) -- cycle;
\node at (11.612,6.425) {\scalebox{1.646}{\small 8}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.998,4.986) -- (6.12,5.005) -- (6.229,5.061) -- (6.317,5.148) -- (6.373,5.258) -- (6.392,5.379) -- (6.373,5.501) -- (6.317,5.611) -- (6.229,5.698) -- (6.12,5.754) -- (5.998,5.773) -- (5.998,5.773) -- (5.876,5.754) -- (5.766,5.698) -- (5.679,5.611) -- (5.623,5.501) -- (5.604,5.379) -- (5.623,5.258) -- (5.679,5.148) -- (5.766,5.061) -- (5.876,5.005) -- (5.998,4.986) -- cycle;
\node at (5.998,5.379) {\scalebox{1.646}{\small 9}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.168,3.212) -- (5.29,3.231) -- (5.4,3.287) -- (5.487,3.374) -- (5.543,3.484) -- (5.562,3.606) -- (5.543,3.727) -- (5.487,3.837) -- (5.4,3.924) -- (5.29,3.98) -- (5.168,3.999) -- (4.798,3.999) -- (4.676,3.98) -- (4.566,3.924) -- (4.479,3.837) -- (4.423,3.727) -- (4.404,3.606) -- (4.423,3.484) -- (4.479,3.374) -- (4.566,3.287) -- (4.676,3.231) -- (4.798,3.212) -- cycle;
\node at (4.983,3.606) {\scalebox{1.646}{\small 10}};
\filldraw[fill=white, draw=black, line width=0.5pt] (11.512,3.007) -- (11.633,3.026) -- (11.743,3.082) -- (11.83,3.17) -- (11.886,3.279) -- (11.906,3.401) -- (11.886,3.523) -- (11.83,3.633) -- (11.743,3.72) -- (11.633,3.776) -- (11.512,3.795) -- (11.141,3.795) -- (11.019,3.776) -- (10.909,3.72) -- (10.822,3.633) -- (10.766,3.523) -- (10.747,3.401) -- (10.766,3.279) -- (10.822,3.17) -- (10.909,3.082) -- (11.019,3.026) -- (11.141,3.007) -- cycle;
\node at (11.326,3.401) {\scalebox{1.646}{\small 11}};
\filldraw[fill=white, draw=black, line width=0.5pt] (9.592,5.007) -- (9.714,5.026) -- (9.823,5.082) -- (9.91,5.169) -- (9.966,5.279) -- (9.986,5.4) -- (9.966,5.522) -- (9.91,5.632) -- (9.823,5.719) -- (9.714,5.775) -- (9.592,5.794) -- (9.221,5.794) -- (9.099,5.775) -- (8.99,5.719) -- (8.902,5.632) -- (8.846,5.522) -- (8.827,5.4) -- (8.846,5.279) -- (8.902,5.169) -- (8.99,5.082) -- (9.099,5.026) -- (9.221,5.007) -- cycle;
\node at (9.406,5.4) {\scalebox{1.646}{\small 12}};
\filldraw[fill=white, draw=black, line width=0.5pt] (7.998,2.748) -- (8.12,2.767) -- (8.229,2.823) -- (8.317,2.91) -- (8.373,3.02) -- (8.392,3.142) -- (8.373,3.264) -- (8.317,3.373) -- (8.229,3.461) -- (8.12,3.516) -- (7.998,3.536) -- (7.627,3.536) -- (7.505,3.516) -- (7.396,3.461) -- (7.309,3.373) -- (7.253,3.264) -- (7.233,3.142) -- (7.253,3.02) -- (7.309,2.91) -- (7.396,2.823) -- (7.505,2.767) -- (7.627,2.748) -- cycle;
\node at (7.813,3.142) {\scalebox{1.646}{\small 13}};
\filldraw[fill=white, draw=black, line width=0.5pt] (2.876,4.309) -- (2.998,4.328) -- (3.107,4.384) -- (3.195,4.471) -- (3.251,4.581) -- (3.27,4.703) -- (3.251,4.825) -- (3.195,4.935) -- (3.107,5.022) -- (2.998,5.078) -- (2.876,5.097) -- (2.505,5.097) -- (2.383,5.078) -- (2.274,5.022) -- (2.187,4.935) -- (2.131,4.825) -- (2.111,4.703) -- (2.131,4.581) -- (2.187,4.471) -- (2.274,4.384) -- (2.383,4.328) -- (2.505,4.309) -- cycle;
\node at (2.691,4.703) {\scalebox{1.646}{\small 14}};
\filldraw[fill=white, draw=black, line width=0.5pt] (2.007,2.872) -- (2.129,2.892) -- (2.239,2.948) -- (2.326,3.035) -- (2.382,3.145) -- (2.401,3.266) -- (2.382,3.388) -- (2.326,3.498) -- (2.239,3.585) -- (2.129,3.641) -- (2.007,3.66) -- (1.637,3.66) -- (1.515,3.641) -- (1.405,3.585) -- (1.318,3.498) -- (1.262,3.388) -- (1.243,3.266) -- (1.262,3.145) -- (1.318,3.035) -- (1.405,2.948) -- (1.515,2.892) -- (1.637,2.872) -- cycle;
\node at (1.822,3.266) {\scalebox{1.646}{\small 15}};
\filldraw[fill=white, draw=black, line width=0.5pt] (3.325,1.087) -- (3.447,1.106) -- (3.557,1.162) -- (3.644,1.249) -- (3.7,1.359) -- (3.719,1.481) -- (3.7,1.603) -- (3.644,1.712) -- (3.557,1.8) -- (3.447,1.855) -- (3.325,1.875) -- (2.955,1.875) -- (2.833,1.855) -- (2.723,1.8) -- (2.636,1.712) -- (2.58,1.603) -- (2.561,1.481) -- (2.58,1.359) -- (2.636,1.249) -- (2.723,1.162) -- (2.833,1.106) -- (2.955,1.087) -- cycle;
\node at (3.14,1.481) {\scalebox{1.646}{\small 16}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.225,1.456) -- (6.347,1.475) -- (6.456,1.531) -- (6.544,1.618) -- (6.599,1.728) -- (6.619,1.85) -- (6.599,1.972) -- (6.544,2.081) -- (6.456,2.169) -- (6.347,2.224) -- (6.225,2.244) -- (5.854,2.244) -- (5.732,2.224) -- (5.623,2.169) -- (5.535,2.081) -- (5.48,1.972) -- (5.46,1.85) -- (5.48,1.728) -- (5.535,1.618) -- (5.623,1.531) -- (5.732,1.475) -- (5.854,1.456) -- cycle;
\node at (6.04,1.85) {\scalebox{1.646}{\small 17}};
\filldraw[fill=white, draw=black, line width=0.5pt] (9.31,1.867) -- (9.432,1.886) -- (9.542,1.942) -- (9.629,2.029) -- (9.685,2.139) -- (9.704,2.261) -- (9.685,2.383) -- (9.629,2.492) -- (9.542,2.58) -- (9.432,2.636) -- (9.31,2.655) -- (8.939,2.655) -- (8.818,2.636) -- (8.708,2.58) -- (8.621,2.492) -- (8.565,2.383) -- (8.545,2.261) -- (8.565,2.139) -- (8.621,2.029) -- (8.708,1.942) -- (8.818,1.886) -- (8.939,1.867) -- cycle;
\node at (9.125,2.261) {\scalebox{1.646}{\small 18}};
\filldraw[fill=yellow!35, draw=black, line width=0.5pt] (7.819,8.136) -- (8.419,8.136) -- (8.419,8.736) -- (7.819,8.736) -- cycle;
\node at (8.119,8.436) {\scalebox{1.646}{\small a}};
\filldraw[fill=red!16, draw=black, line width=0.5pt] (4.72,5.422) -- (5.32,5.422) -- (5.32,6.022) -- (4.72,6.022) -- cycle;
\node at (5.02,5.722) {\scalebox{1.646}{\small b}};
\filldraw[fill=black!14, draw=black, line width=0.5pt] (3.482,2.79) -- (4.082,2.79) -- (4.082,3.39) -- (3.482,3.39) -- cycle;
\node at (3.782,3.09) {\scalebox{1.646}{\small c}};
\filldraw[fill=black!14, draw=black, line width=0.5pt] (1.304,5.211) -- (1.904,5.211) -- (1.904,5.811) -- (1.304,5.811) -- cycle;
\node at (1.604,5.511) {\scalebox{1.646}{\small d}};
\node at (11.675,12.043) {\scalebox{1.646}{\small A}};
\node at (3.729,9.22) {\scalebox{1.646}{\small B}};
\node at (8.412,8.982) {\scalebox{1.646}{\small C}};
\node at (0.868,8.561) {\scalebox{1.646}{\small D}};
\node at (11.548,8.106) {\scalebox{1.646}{\small E}};
\node at (3.604,5.508) {\scalebox{1.646}{\small F}};
\node at (11.82,4.884) {\scalebox{1.646}{\small G}};
\node at (8.185,4.426) {\scalebox{1.646}{\small H}};
\node at (0.765,4.435) {\scalebox{1.646}{\small I}};
\node at (1.207,1.545) {\scalebox{1.646}{\small J}};
\node at (11.395,1.501) {\scalebox{1.646}{\small K}};
\node at (4.363,1.031) {\scalebox{1.646}{\small L}};
\node at (7.574,0.95) {\scalebox{1.646}{\small M}};
\draw[line width=0.5pt] (12.592,10.605) -- (12.592,11.705);
\draw[line width=0.5pt] (12.361,11.32) -- (12.592,11.705) -- (12.823,11.32);
\draw[line width=0.5pt] (12.29,11.155) -- (12.895,11.155);
\node at (12.592,12.09) {\scalebox{1.646}{\small N}};
\end{tikzpicture}
\end{center}
\noindent \textbf{Le car part de l'école, au carrefour C, et doit s'arrêter à chaque carrefour exactement une fois.} Il emprunte les rues qu'il veut et n'a pas à toutes les parcourir.\par\addvspace{0.35em}
\begin{center}
\renewcommand{\arraystretch}{1.35}
\begin{tabular}{|c|c|c|c|}
\hline
\cellcolor{black!32}\bfseries Les rues & ⑩ rue de la Mairie & Ⓐ Place Sainte-Croix & Ⓚ Place de la Fontaine \\ \hline
① impasse des Roses & ⑪ rue Neuve & Ⓑ Rond-point de la Gare & Ⓛ Carrefour du Moulin \\ \hline
② rue du Stade & ⑫ chemin des Vignes & Ⓒ Carrefour du Lavoir & Ⓜ Carrefour Saint-Roch \\ \hline
③ rue de l'Église & ⑬ boulevard du Parc & Ⓓ Placette des Ormes & \cellcolor{black!32}\bfseries Les bâtiments \\ \hline
④ rue Verte & ⑭ rue du Moulin & Ⓔ Rond-point de la Poste & \textbf{a} l'école \\ \hline
⑤ venelle du Chat & ⑮ allée des Tilleuls & Ⓕ Carrefour de la Mairie & \textbf{b} la pharmacie \\ \hline
⑥ quai aux Fleurs & ⑯ passage du Marché & Ⓖ Rond-point du Pont & \textbf{c} le gymnase \\ \hline
⑦ allée des Peupliers & ⑰ rue du Puits & Ⓗ Carrefour des Tilleuls & \textbf{d} le cimetière \\ \hline
⑧ chemin de Ronde & ⑱ chemin Creux & Ⓘ Carrefour de l'Hôpital &  \\ \hline
⑨ sentier des Prés & \cellcolor{black!32}\bfseries Les carrefours & Ⓙ Coin du Lavoir &  \\ \hline
\end{tabular}
\end{center}
\noindent{\small\itshape Légende du plan}\par\addvspace{0.4em}
\begin{enumerate}
  \item Colorier les carrefours du plan avec \textbf{deux couleurs}, de sorte que deux carrefours \textbf{reliés par une rue} ne soient jamais de la même couleur. Combien y en a-t-il de chaque couleur ?
  \item Le car roule d'un carrefour au suivant. Que peut-on dire de la \textbf{couleur} des arrêts successifs ? Qu'en déduire sur les couleurs des arrêts d'une tournée qui les dessert tous ?
  \item \textbf{Le car peut-il desservir tous les carrefours, une fois chacun, et revenir à l'école ?} Si oui, décrire un trajet ; sinon, démontrer que c'est impossible.
  \item \textbf{Et s'il n'est pas obligé de revenir à l'école ?} Même consigne.
\end{enumerate}
\newpage
\section*{\textcolor{red}{Correction}}
\needspace{5\baselineskip}
\subsection*{\textcolor{red}{Le car de ramassage — Correction}}
\needspace{3\baselineskip}
\begin{center}
\begin{tikzpicture}[scale=0.6225, line join=round, line cap=round]
\draw[line width=0.5pt] (11.292,11.555) -- (11.231,11.293) -- (11.175,11.03) -- (11.126,10.766) -- (11.083,10.501) -- (11.046,10.234) -- (11.015,9.967) -- (10.991,9.699) -- (10.973,9.431) -- (10.961,9.162) -- (10.956,8.893) -- (10.957,8.625) -- (10.964,8.356) -- (10.978,8.088) -- (10.998,7.82);
\draw[line width=0.5pt] (4.103,8.726) -- (4.391,8.749) -- (4.679,8.766) -- (4.968,8.776) -- (5.257,8.778) -- (5.546,8.775) -- (5.835,8.764) -- (6.123,8.747) -- (6.411,8.722) -- (6.698,8.691) -- (6.985,8.654) -- (7.27,8.609) -- (7.555,8.558) -- (7.838,8.5) -- (8.119,8.436);
\draw[line width=0.5pt] (4.103,8.726) -- (4.077,8.496) -- (4.055,8.266) -- (4.04,8.036) -- (4.029,7.805) -- (4.024,7.574) -- (4.025,7.342) -- (4.031,7.111) -- (4.042,6.88) -- (4.059,6.65) -- (4.081,6.419) -- (4.109,6.19) -- (4.142,5.961) -- (4.18,5.733) -- (4.224,5.507);
\draw[line width=0.5pt] (8.119,8.436) -- (8.33,8.424) -- (8.54,8.407) -- (8.75,8.384) -- (8.96,8.357) -- (9.169,8.325) -- (9.377,8.288) -- (9.584,8.247) -- (9.79,8.2) -- (9.995,8.148) -- (10.198,8.092) -- (10.401,8.031) -- (10.601,7.965) -- (10.8,7.895) -- (10.998,7.82);
\draw[line width=0.5pt] (8.119,8.436) -- (8.047,8.181) -- (7.981,7.924) -- (7.921,7.666) -- (7.867,7.406) -- (7.819,7.145) -- (7.777,6.883) -- (7.742,6.62) -- (7.712,6.356) -- (7.689,6.092) -- (7.672,5.827) -- (7.661,5.562) -- (7.657,5.296) -- (7.659,5.031) -- (7.667,4.766);
\draw[line width=0.5pt] (1.414,8.267) -- (1.599,8.329) -- (1.787,8.387) -- (1.975,8.44) -- (2.165,8.489) -- (2.355,8.533) -- (2.547,8.572) -- (2.74,8.608) -- (2.933,8.638) -- (3.127,8.664) -- (3.322,8.686) -- (3.517,8.703) -- (3.712,8.715) -- (3.908,8.723) -- (4.103,8.726);
\draw[line width=0.5pt] (1.414,8.267) -- (1.37,8.004) -- (1.333,7.74) -- (1.302,7.475) -- (1.277,7.209) -- (1.259,6.943) -- (1.247,6.676) -- (1.241,6.409) -- (1.241,6.142) -- (1.248,5.875) -- (1.261,5.608) -- (1.28,5.342) -- (1.305,5.076) -- (1.337,4.811) -- (1.375,4.547);
\draw[line width=0.5pt] (10.998,7.82) -- (11.044,7.619) -- (11.085,7.417) -- (11.121,7.215) -- (11.153,7.011) -- (11.18,6.807) -- (11.202,6.602) -- (11.219,6.396) -- (11.231,6.191) -- (11.239,5.985) -- (11.241,5.779) -- (11.239,5.573) -- (11.232,5.367) -- (11.22,5.161) -- (11.204,4.956);
\draw[line width=0.5pt] (4.224,5.507) -- (4.46,5.416) -- (4.698,5.332) -- (4.938,5.253) -- (5.18,5.18) -- (5.423,5.112) -- (5.669,5.05) -- (5.915,4.994) -- (6.163,4.944) -- (6.412,4.9) -- (6.661,4.861) -- (6.912,4.828) -- (7.163,4.802) -- (7.415,4.781) -- (7.667,4.766);
\draw[line width=0.5pt] (4.224,5.507) -- (4.296,5.233) -- (4.362,4.959) -- (4.421,4.682) -- (4.473,4.404) -- (4.519,4.125) -- (4.558,3.845) -- (4.591,3.564) -- (4.617,3.283) -- (4.637,3.001) -- (4.65,2.718) -- (4.656,2.436) -- (4.656,2.153) -- (4.649,1.871) -- (4.635,1.588);
\draw[line width=0.5pt] (11.204,4.956) -- (11.15,4.742) -- (11.101,4.527) -- (11.058,4.311) -- (11.019,4.094) -- (10.986,3.876) -- (10.957,3.657) -- (10.934,3.438) -- (10.916,3.218) -- (10.903,2.998) -- (10.896,2.777) -- (10.893,2.557) -- (10.896,2.336) -- (10.904,2.116) -- (10.917,1.896);
\draw[line width=0.5pt] (7.667,4.766) -- (7.916,4.818) -- (8.165,4.865) -- (8.416,4.905) -- (8.668,4.939) -- (8.921,4.968) -- (9.174,4.99) -- (9.428,5.007) -- (9.682,5.018) -- (9.936,5.022) -- (10.19,5.021) -- (10.444,5.014) -- (10.698,5.001) -- (10.951,4.981) -- (11.204,4.956);
\draw[line width=0.5pt] (7.667,4.766) -- (7.616,4.541) -- (7.57,4.315) -- (7.529,4.088) -- (7.493,3.859) -- (7.463,3.63) -- (7.439,3.4) -- (7.42,3.17) -- (7.406,2.939) -- (7.398,2.708) -- (7.395,2.477) -- (7.397,2.246) -- (7.405,2.015) -- (7.418,1.785) -- (7.437,1.555);
\draw[line width=0.5pt] (1.375,4.547) -- (1.566,4.646) -- (1.76,4.741) -- (1.956,4.831) -- (2.154,4.917) -- (2.354,4.997) -- (2.556,5.073) -- (2.76,5.145) -- (2.965,5.211) -- (3.172,5.273) -- (3.38,5.329) -- (3.59,5.381) -- (3.8,5.428) -- (4.012,5.47) -- (4.224,5.507);
\draw[line width=0.5pt] (1.375,4.547) -- (1.369,4.357) -- (1.368,4.167) -- (1.372,3.976) -- (1.38,3.786) -- (1.393,3.596) -- (1.41,3.407) -- (1.431,3.217) -- (1.457,3.029) -- (1.488,2.841) -- (1.522,2.653) -- (1.561,2.467) -- (1.605,2.282) -- (1.653,2.097) -- (1.705,1.915);
\draw[line width=0.5pt] (1.705,1.915) -- (1.916,1.923) -- (2.128,1.927) -- (2.339,1.926) -- (2.551,1.92) -- (2.762,1.909) -- (2.973,1.893) -- (3.183,1.872) -- (3.394,1.846) -- (3.603,1.816) -- (3.811,1.78) -- (4.019,1.739) -- (4.226,1.694) -- (4.431,1.644) -- (4.635,1.588);
\draw[line width=0.5pt] (4.635,1.588) -- (4.833,1.555) -- (5.032,1.527) -- (5.232,1.503) -- (5.432,1.484) -- (5.633,1.47) -- (5.834,1.461) -- (6.035,1.456) -- (6.236,1.456) -- (6.437,1.461) -- (6.638,1.47) -- (6.839,1.484) -- (7.039,1.503) -- (7.238,1.526) -- (7.437,1.555);
\draw[line width=0.5pt] (7.437,1.555) -- (7.68,1.617) -- (7.924,1.673) -- (8.17,1.724) -- (8.417,1.769) -- (8.665,1.808) -- (8.914,1.841) -- (9.163,1.869) -- (9.413,1.89) -- (9.664,1.906) -- (9.914,1.916) -- (10.165,1.92) -- (10.416,1.918) -- (10.667,1.91) -- (10.917,1.896);
\filldraw[fill=black!38, draw=black, line width=0.5pt] (11.666,11.555) -- (11.637,11.698) -- (11.556,11.819) -- (11.435,11.9) -- (11.292,11.928) -- (11.149,11.9) -- (11.028,11.819) -- (10.948,11.698) -- (10.919,11.555) -- (10.948,11.412) -- (11.028,11.291) -- (11.149,11.21) -- (11.292,11.182) -- (11.435,11.21) -- (11.556,11.291) -- (11.637,11.412) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (4.477,8.726) -- (4.448,8.869) -- (4.367,8.99) -- (4.246,9.071) -- (4.103,9.099) -- (3.961,9.071) -- (3.839,8.99) -- (3.759,8.869) -- (3.73,8.726) -- (3.759,8.583) -- (3.839,8.462) -- (3.961,8.381) -- (4.103,8.353) -- (4.246,8.381) -- (4.367,8.462) -- (4.448,8.583) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (8.492,8.436) -- (8.464,8.579) -- (8.383,8.7) -- (8.262,8.781) -- (8.119,8.809) -- (7.976,8.781) -- (7.855,8.7) -- (7.774,8.579) -- (7.746,8.436) -- (7.774,8.293) -- (7.855,8.172) -- (7.976,8.091) -- (8.119,8.063) -- (8.262,8.091) -- (8.383,8.172) -- (8.464,8.293) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (1.787,8.267) -- (1.759,8.41) -- (1.678,8.531) -- (1.557,8.612) -- (1.414,8.641) -- (1.271,8.612) -- (1.15,8.531) -- (1.069,8.41) -- (1.041,8.267) -- (1.069,8.125) -- (1.15,8.004) -- (1.271,7.923) -- (1.414,7.894) -- (1.557,7.923) -- (1.678,8.004) -- (1.759,8.125) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (11.371,7.82) -- (11.342,7.962) -- (11.262,8.084) -- (11.14,8.164) -- (10.998,8.193) -- (10.855,8.164) -- (10.734,8.084) -- (10.653,7.962) -- (10.624,7.82) -- (10.653,7.677) -- (10.734,7.556) -- (10.855,7.475) -- (10.998,7.446) -- (11.14,7.475) -- (11.262,7.556) -- (11.342,7.677) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (4.597,5.507) -- (4.569,5.649) -- (4.488,5.771) -- (4.367,5.851) -- (4.224,5.88) -- (4.081,5.851) -- (3.96,5.771) -- (3.879,5.649) -- (3.851,5.507) -- (3.879,5.364) -- (3.96,5.243) -- (4.081,5.162) -- (4.224,5.133) -- (4.367,5.162) -- (4.488,5.243) -- (4.569,5.364) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (11.577,4.956) -- (11.549,5.099) -- (11.468,5.22) -- (11.347,5.301) -- (11.204,5.329) -- (11.061,5.301) -- (10.94,5.22) -- (10.859,5.099) -- (10.831,4.956) -- (10.859,4.813) -- (10.94,4.692) -- (11.061,4.611) -- (11.204,4.583) -- (11.347,4.611) -- (11.468,4.692) -- (11.549,4.813) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (8.04,4.766) -- (8.012,4.909) -- (7.931,5.03) -- (7.81,5.111) -- (7.667,5.139) -- (7.524,5.111) -- (7.403,5.03) -- (7.322,4.909) -- (7.294,4.766) -- (7.322,4.623) -- (7.403,4.502) -- (7.524,4.421) -- (7.667,4.393) -- (7.81,4.421) -- (7.931,4.502) -- (8.012,4.623) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (1.748,4.547) -- (1.719,4.69) -- (1.639,4.811) -- (1.518,4.892) -- (1.375,4.921) -- (1.232,4.892) -- (1.111,4.811) -- (1.03,4.69) -- (1.001,4.547) -- (1.03,4.404) -- (1.111,4.283) -- (1.232,4.203) -- (1.375,4.174) -- (1.518,4.203) -- (1.639,4.283) -- (1.719,4.404) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (2.078,1.915) -- (2.05,2.057) -- (1.969,2.178) -- (1.848,2.259) -- (1.705,2.288) -- (1.562,2.259) -- (1.441,2.178) -- (1.36,2.057) -- (1.332,1.915) -- (1.36,1.772) -- (1.441,1.651) -- (1.562,1.57) -- (1.705,1.541) -- (1.848,1.57) -- (1.969,1.651) -- (2.05,1.772) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (11.29,1.896) -- (11.262,2.039) -- (11.181,2.16) -- (11.06,2.241) -- (10.917,2.269) -- (10.774,2.241) -- (10.653,2.16) -- (10.572,2.039) -- (10.544,1.896) -- (10.572,1.753) -- (10.653,1.632) -- (10.774,1.551) -- (10.917,1.523) -- (11.06,1.551) -- (11.181,1.632) -- (11.262,1.753) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (5.008,1.588) -- (4.98,1.731) -- (4.899,1.852) -- (4.778,1.933) -- (4.635,1.962) -- (4.492,1.933) -- (4.371,1.852) -- (4.29,1.731) -- (4.262,1.588) -- (4.29,1.446) -- (4.371,1.324) -- (4.492,1.244) -- (4.635,1.215) -- (4.778,1.244) -- (4.899,1.324) -- (4.98,1.446) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (7.81,1.555) -- (7.782,1.698) -- (7.701,1.819) -- (7.58,1.9) -- (7.437,1.928) -- (7.294,1.9) -- (7.173,1.819) -- (7.092,1.698) -- (7.064,1.555) -- (7.092,1.412) -- (7.173,1.291) -- (7.294,1.21) -- (7.437,1.182) -- (7.58,1.21) -- (7.701,1.291) -- (7.782,1.412) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (11.374,9.285) -- (11.493,9.303) -- (11.6,9.358) -- (11.685,9.443) -- (11.74,9.55) -- (11.759,9.669) -- (11.74,9.788) -- (11.685,9.895) -- (11.6,9.98) -- (11.493,10.035) -- (11.374,10.054) -- (11.374,10.054) -- (11.255,10.035) -- (11.148,9.98) -- (11.063,9.895) -- (11.009,9.788) -- (10.99,9.669) -- (11.009,9.55) -- (11.063,9.443) -- (11.148,9.358) -- (11.255,9.303) -- (11.374,9.285) -- cycle;
\node at (11.374,9.669) {\scalebox{1.606}{\small 1}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.151,8.746) -- (6.27,8.764) -- (6.377,8.819) -- (6.462,8.904) -- (6.516,9.011) -- (6.535,9.13) -- (6.516,9.249) -- (6.462,9.356) -- (6.377,9.441) -- (6.27,9.496) -- (6.151,9.515) -- (6.151,9.515) -- (6.032,9.496) -- (5.925,9.441) -- (5.84,9.356) -- (5.785,9.249) -- (5.766,9.13) -- (5.785,9.011) -- (5.84,8.904) -- (5.925,8.819) -- (6.032,8.764) -- (6.151,8.746) -- cycle;
\node at (6.151,9.13) {\scalebox{1.606}{\small 2}};
\filldraw[fill=white, draw=black, line width=0.5pt] (4.415,6.741) -- (4.534,6.76) -- (4.641,6.815) -- (4.726,6.9) -- (4.781,7.007) -- (4.8,7.126) -- (4.781,7.244) -- (4.726,7.352) -- (4.641,7.437) -- (4.534,7.491) -- (4.415,7.51) -- (4.415,7.51) -- (4.296,7.491) -- (4.189,7.437) -- (4.104,7.352) -- (4.05,7.244) -- (4.031,7.126) -- (4.05,7.007) -- (4.104,6.9) -- (4.189,6.815) -- (4.296,6.76) -- (4.415,6.741) -- cycle;
\node at (4.415,7.126) {\scalebox{1.606}{\small 3}};
\filldraw[fill=white, draw=black, line width=0.5pt] (9.664,8.238) -- (9.783,8.257) -- (9.89,8.311) -- (9.975,8.397) -- (10.03,8.504) -- (10.049,8.623) -- (10.03,8.741) -- (9.975,8.849) -- (9.89,8.934) -- (9.783,8.988) -- (9.664,9.007) -- (9.664,9.007) -- (9.545,8.988) -- (9.438,8.934) -- (9.353,8.849) -- (9.299,8.741) -- (9.28,8.623) -- (9.299,8.504) -- (9.353,8.397) -- (9.438,8.311) -- (9.545,8.257) -- (9.664,8.238) -- cycle;
\node at (9.664,8.623) {\scalebox{1.606}{\small 4}};
\filldraw[fill=white, draw=black, line width=0.5pt] (8.123,6.188) -- (8.242,6.207) -- (8.349,6.262) -- (8.434,6.347) -- (8.489,6.454) -- (8.508,6.573) -- (8.489,6.692) -- (8.434,6.799) -- (8.349,6.884) -- (8.242,6.938) -- (8.123,6.957) -- (8.123,6.957) -- (8.004,6.938) -- (7.897,6.884) -- (7.812,6.799) -- (7.758,6.692) -- (7.739,6.573) -- (7.758,6.454) -- (7.812,6.347) -- (7.897,6.262) -- (8.004,6.207) -- (8.123,6.188) -- cycle;
\node at (8.123,6.573) {\scalebox{1.606}{\small 5}};
\filldraw[fill=white, draw=black, line width=0.5pt] (2.675,8.602) -- (2.794,8.621) -- (2.901,8.675) -- (2.986,8.761) -- (3.041,8.868) -- (3.06,8.987) -- (3.041,9.105) -- (2.986,9.213) -- (2.901,9.298) -- (2.794,9.352) -- (2.675,9.371) -- (2.675,9.371) -- (2.556,9.352) -- (2.449,9.298) -- (2.364,9.213) -- (2.309,9.105) -- (2.291,8.987) -- (2.309,8.868) -- (2.364,8.761) -- (2.449,8.675) -- (2.556,8.621) -- (2.675,8.602) -- cycle;
\node at (2.675,8.987) {\scalebox{1.606}{\small 6}};
\filldraw[fill=white, draw=black, line width=0.5pt] (1.625,6.02) -- (1.744,6.039) -- (1.851,6.094) -- (1.936,6.179) -- (1.991,6.286) -- (2.01,6.405) -- (1.991,6.524) -- (1.936,6.631) -- (1.851,6.716) -- (1.744,6.771) -- (1.625,6.789) -- (1.625,6.789) -- (1.507,6.771) -- (1.399,6.716) -- (1.314,6.631) -- (1.26,6.524) -- (1.241,6.405) -- (1.26,6.286) -- (1.314,6.179) -- (1.399,6.094) -- (1.507,6.039) -- (1.625,6.02) -- cycle;
\node at (1.625,6.405) {\scalebox{1.606}{\small 7}};
\filldraw[fill=white, draw=black, line width=0.5pt] (11.602,6.04) -- (11.721,6.058) -- (11.828,6.113) -- (11.913,6.198) -- (11.968,6.305) -- (11.987,6.424) -- (11.968,6.543) -- (11.913,6.65) -- (11.828,6.735) -- (11.721,6.79) -- (11.602,6.809) -- (11.602,6.809) -- (11.484,6.79) -- (11.376,6.735) -- (11.291,6.65) -- (11.237,6.543) -- (11.218,6.424) -- (11.237,6.305) -- (11.291,6.198) -- (11.376,6.113) -- (11.484,6.058) -- (11.602,6.04) -- cycle;
\node at (11.602,6.424) {\scalebox{1.606}{\small 8}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.996,4.986) -- (6.115,5.005) -- (6.222,5.059) -- (6.307,5.144) -- (6.362,5.251) -- (6.38,5.37) -- (6.362,5.489) -- (6.307,5.596) -- (6.222,5.681) -- (6.115,5.736) -- (5.996,5.755) -- (5.996,5.755) -- (5.877,5.736) -- (5.77,5.681) -- (5.685,5.596) -- (5.63,5.489) -- (5.611,5.37) -- (5.63,5.251) -- (5.685,5.144) -- (5.77,5.059) -- (5.877,5.005) -- (5.996,4.986) -- cycle;
\node at (5.996,5.37) {\scalebox{1.606}{\small 9}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.155,3.22) -- (5.273,3.239) -- (5.381,3.293) -- (5.466,3.379) -- (5.52,3.486) -- (5.539,3.605) -- (5.52,3.723) -- (5.466,3.831) -- (5.381,3.916) -- (5.273,3.97) -- (5.155,3.989) -- (4.793,3.989) -- (4.674,3.97) -- (4.567,3.916) -- (4.482,3.831) -- (4.427,3.723) -- (4.408,3.605) -- (4.427,3.486) -- (4.482,3.379) -- (4.567,3.293) -- (4.674,3.239) -- (4.793,3.22) -- cycle;
\node at (4.974,3.605) {\scalebox{1.606}{\small 10}};
\filldraw[fill=white, draw=black, line width=0.5pt] (11.498,3.017) -- (11.617,3.036) -- (11.724,3.091) -- (11.809,3.176) -- (11.864,3.283) -- (11.882,3.402) -- (11.864,3.521) -- (11.809,3.628) -- (11.724,3.713) -- (11.617,3.768) -- (11.498,3.787) -- (11.136,3.787) -- (11.017,3.768) -- (10.91,3.713) -- (10.825,3.628) -- (10.77,3.521) -- (10.752,3.402) -- (10.77,3.283) -- (10.825,3.176) -- (10.91,3.091) -- (11.017,3.036) -- (11.136,3.017) -- cycle;
\node at (11.317,3.402) {\scalebox{1.606}{\small 11}};
\filldraw[fill=white, draw=black, line width=0.5pt] (9.588,5.007) -- (9.707,5.025) -- (9.814,5.08) -- (9.899,5.165) -- (9.954,5.272) -- (9.972,5.391) -- (9.954,5.51) -- (9.899,5.617) -- (9.814,5.702) -- (9.707,5.757) -- (9.588,5.776) -- (9.226,5.776) -- (9.107,5.757) -- (9.0,5.702) -- (8.915,5.617) -- (8.86,5.51) -- (8.841,5.391) -- (8.86,5.272) -- (8.915,5.165) -- (9.0,5.08) -- (9.107,5.025) -- (9.226,5.007) -- cycle;
\node at (9.407,5.391) {\scalebox{1.606}{\small 12}};
\filldraw[fill=white, draw=black, line width=0.5pt] (7.984,2.758) -- (8.103,2.777) -- (8.21,2.831) -- (8.295,2.916) -- (8.35,3.024) -- (8.369,3.143) -- (8.35,3.261) -- (8.295,3.369) -- (8.21,3.454) -- (8.103,3.508) -- (7.984,3.527) -- (7.622,3.527) -- (7.503,3.508) -- (7.396,3.454) -- (7.311,3.369) -- (7.257,3.261) -- (7.238,3.143) -- (7.257,3.024) -- (7.311,2.916) -- (7.396,2.831) -- (7.503,2.777) -- (7.622,2.758) -- cycle;
\node at (7.803,3.143) {\scalebox{1.606}{\small 13}};
\filldraw[fill=white, draw=black, line width=0.5pt] (2.868,4.327) -- (2.987,4.346) -- (3.094,4.401) -- (3.179,4.486) -- (3.234,4.593) -- (3.253,4.712) -- (3.234,4.831) -- (3.179,4.938) -- (3.094,5.023) -- (2.987,5.078) -- (2.868,5.096) -- (2.506,5.096) -- (2.388,5.078) -- (2.28,5.023) -- (2.195,4.938) -- (2.141,4.831) -- (2.122,4.712) -- (2.141,4.593) -- (2.195,4.486) -- (2.28,4.401) -- (2.388,4.346) -- (2.506,4.327) -- cycle;
\node at (2.687,4.712) {\scalebox{1.606}{\small 14}};
\filldraw[fill=white, draw=black, line width=0.5pt] (1.994,2.881) -- (2.113,2.899) -- (2.22,2.954) -- (2.305,3.039) -- (2.359,3.146) -- (2.378,3.265) -- (2.359,3.384) -- (2.305,3.491) -- (2.22,3.576) -- (2.113,3.631) -- (1.994,3.65) -- (1.632,3.65) -- (1.513,3.631) -- (1.406,3.576) -- (1.321,3.491) -- (1.266,3.384) -- (1.247,3.265) -- (1.266,3.146) -- (1.321,3.039) -- (1.406,2.954) -- (1.513,2.899) -- (1.632,2.881) -- cycle;
\node at (1.813,3.265) {\scalebox{1.606}{\small 15}};
\filldraw[fill=white, draw=black, line width=0.5pt] (3.322,1.106) -- (3.441,1.124) -- (3.548,1.179) -- (3.633,1.264) -- (3.688,1.371) -- (3.706,1.49) -- (3.688,1.609) -- (3.633,1.716) -- (3.548,1.801) -- (3.441,1.856) -- (3.322,1.875) -- (2.96,1.875) -- (2.841,1.856) -- (2.734,1.801) -- (2.649,1.716) -- (2.594,1.609) -- (2.575,1.49) -- (2.594,1.371) -- (2.649,1.264) -- (2.734,1.179) -- (2.841,1.124) -- (2.96,1.106) -- cycle;
\node at (3.141,1.49) {\scalebox{1.606}{\small 16}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.22,1.456) -- (6.339,1.475) -- (6.446,1.529) -- (6.531,1.614) -- (6.586,1.722) -- (6.605,1.84) -- (6.586,1.959) -- (6.531,2.066) -- (6.446,2.152) -- (6.339,2.206) -- (6.22,2.225) -- (5.858,2.225) -- (5.74,2.206) -- (5.632,2.152) -- (5.547,2.066) -- (5.493,1.959) -- (5.474,1.84) -- (5.493,1.722) -- (5.547,1.614) -- (5.632,1.529) -- (5.74,1.475) -- (5.858,1.456) -- cycle;
\node at (6.039,1.84) {\scalebox{1.606}{\small 17}};
\filldraw[fill=white, draw=black, line width=0.5pt] (9.306,1.867) -- (9.425,1.886) -- (9.533,1.94) -- (9.618,2.026) -- (9.672,2.133) -- (9.691,2.252) -- (9.672,2.37) -- (9.618,2.478) -- (9.533,2.563) -- (9.425,2.617) -- (9.306,2.636) -- (8.945,2.636) -- (8.826,2.617) -- (8.719,2.563) -- (8.634,2.478) -- (8.579,2.37) -- (8.56,2.252) -- (8.579,2.133) -- (8.634,2.026) -- (8.719,1.94) -- (8.826,1.886) -- (8.945,1.867) -- cycle;
\node at (9.126,2.252) {\scalebox{1.606}{\small 18}};
\filldraw[fill=yellow!35, draw=black, line width=0.5pt] (7.819,8.136) -- (8.419,8.136) -- (8.419,8.736) -- (7.819,8.736) -- cycle;
\node at (8.119,8.436) {\scalebox{1.606}{\small a}};
\filldraw[fill=red!16, draw=black, line width=0.5pt] (4.72,5.422) -- (5.32,5.422) -- (5.32,6.022) -- (4.72,6.022) -- cycle;
\node at (5.02,5.722) {\scalebox{1.606}{\small b}};
\filldraw[fill=black!14, draw=black, line width=0.5pt] (3.482,2.79) -- (4.082,2.79) -- (4.082,3.39) -- (3.482,3.39) -- cycle;
\node at (3.782,3.09) {\scalebox{1.606}{\small c}};
\filldraw[fill=black!14, draw=black, line width=0.5pt] (1.304,5.211) -- (1.904,5.211) -- (1.904,5.811) -- (1.304,5.811) -- cycle;
\node at (1.604,5.511) {\scalebox{1.606}{\small d}};
\node at (11.675,12.043) {\scalebox{1.606}{\small A}};
\node at (3.729,9.22) {\scalebox{1.606}{\small B}};
\node at (8.412,8.982) {\scalebox{1.606}{\small C}};
\node at (0.868,8.561) {\scalebox{1.606}{\small D}};
\node at (11.548,8.106) {\scalebox{1.606}{\small E}};
\node at (3.604,5.508) {\scalebox{1.606}{\small F}};
\node at (11.82,4.884) {\scalebox{1.606}{\small G}};
\node at (8.185,4.426) {\scalebox{1.606}{\small H}};
\node at (0.765,4.435) {\scalebox{1.606}{\small I}};
\node at (1.207,1.545) {\scalebox{1.606}{\small J}};
\node at (11.395,1.501) {\scalebox{1.606}{\small K}};
\node at (4.363,1.031) {\scalebox{1.606}{\small L}};
\node at (7.574,0.95) {\scalebox{1.606}{\small M}};
\draw[line width=0.5pt] (12.592,10.605) -- (12.592,11.705);
\draw[line width=0.5pt] (12.361,11.32) -- (12.592,11.705) -- (12.823,11.32);
\draw[line width=0.5pt] (12.29,11.155) -- (12.895,11.155);
\node at (12.592,12.09) {\scalebox{1.606}{\small N}};
\end{tikzpicture}
\end{center}
\noindent{\small\itshape Deux carrefours reliés par une rue n'ont jamais la même couleur.}\par\addvspace{0.4em}
\noindent \textbf{1.} Le coloriage est \textbf{forcé} : une fois la couleur d'un carrefour choisie, celle de tous les autres suit, de proche en proche.\par\addvspace{0.35em}
\begin{center}
\renewcommand{\arraystretch}{1.35}
\begin{tabular}{|c|c|c|}
\hline
\cellcolor{blue!7}\bfseries Couleur & \cellcolor{blue!7}\bfseries Carrefours & \cellcolor{blue!7}\bfseries Nombre \\ \hline
sombres & A, C, D, F, G, J, M & 7 \\ \hline
clairs & B, E, H, I, K, L & 6 \\ \hline
\end{tabular}
\end{center}
\noindent{\color{red!80!black}\bfseries Il y a \textbf{7} carrefours sombres et \textbf{6} clairs. Il y en a donc \textbf{1 de plus} du côté des sombres.}\par\addvspace{0.4em}
\noindent \textbf{2.}\par\addvspace{0.35em}
\noindent{\color{green!45!black}\textbf{Le raisonnement clé.} Chaque rue relie un carrefour sombre à un carrefour clair. Donc à chaque fois que le car roule, il \textbf{change de couleur} : ses arrêts sont sombre, clair, sombre, clair\dots{} \textbf{en alternance}.}\par\addvspace{0.4em}
\noindent{\color{red!80!black}\bfseries Une tournée qui dessert les 13 carrefours alterne donc les deux couleurs d'un bout à l'autre : elle en utilise \textbf{autant de chaque, à un près}. Et si elle en utilise un de plus d'une couleur, c'est forcément celle de son \textbf{départ} et de son \textbf{arrivée}.}\par\addvspace{0.4em}
\noindent \textbf{3.}\par\addvspace{0.35em}
\noindent{\color{red!80!black}\bfseries \textbf{Non.} Un circuit revient à son point de départ : il compte autant d'arrêts sombres que de clairs. Or ce quartier a 7 carrefours sombres et 6 clairs — c'est impossible.}\par\addvspace{0.4em}
\noindent \textbf{4.}\par\addvspace{0.35em}
\noindent{\color{red!80!black}\bfseries \textbf{Oui}, à condition de ne pas revenir. Un trajet possible au départ de \textbf{C} :}\par\addvspace{0.4em}
\newpage
\noindent \textbf{Le trajet du car}\par\addvspace{0.35em}
\noindent Le car sort de l'école et prend la \textbf{rue du Stade ②} vers l'ouest jusqu'à Rond-point de la Gare \textbf{(B)}.\par\addvspace{0.35em}
\noindent Il continue tout droit dans le \textbf{quai aux Fleurs ⑥}, vers l'ouest, jusqu'à Placette des Ormes \textbf{(D)}.\par\addvspace{0.35em}
\noindent Il tourne à gauche dans l'\textbf{allée des Peupliers ⑦}, vers le sud, jusqu'à Carrefour de l'Hôpital \textbf{(I)}.\par\addvspace{0.35em}
\noindent Il continue tout droit dans l'\textbf{allée des Tilleuls ⑮}, vers le sud, jusqu'à Coin du Lavoir \textbf{(J)}.\par\addvspace{0.35em}
\noindent Il tourne à gauche dans le \textbf{passage du Marché ⑯}, vers l'est, jusqu'à Carrefour du Moulin \textbf{(L)}.\par\addvspace{0.35em}
\noindent Il tourne à gauche dans la \textbf{rue de la Mairie ⑩}, vers le nord, jusqu'à Carrefour de la Mairie \textbf{(F)}.\par\addvspace{0.35em}
\noindent Il tourne à droite dans le \textbf{sentier des Prés ⑨}, vers l'est, jusqu'à Carrefour des Tilleuls \textbf{(H)}.\par\addvspace{0.35em}
\noindent Il tourne à droite dans le \textbf{boulevard du Parc ⑬}, vers le sud, jusqu'à Carrefour Saint-Roch \textbf{(M)}.\par\addvspace{0.35em}
\noindent Il tourne à gauche dans le \textbf{chemin Creux ⑱}, vers l'est, jusqu'à Place de la Fontaine \textbf{(K)}.\par\addvspace{0.35em}
\noindent Il tourne à gauche dans la \textbf{rue Neuve ⑪}, vers le nord, jusqu'à Rond-point du Pont \textbf{(G)}.\par\addvspace{0.35em}
\noindent Il continue tout droit dans le \textbf{chemin de Ronde ⑧}, vers le nord, jusqu'à Rond-point de la Poste \textbf{(E)}.\par\addvspace{0.35em}
\noindent Il continue tout droit dans l'\textbf{impasse des Roses ①}, vers le nord, jusqu'à Place Sainte-Croix \textbf{(A)}.\par\addvspace{0.35em}
\noindent{\color{red!80!black}\bfseries Les 13 carrefours ont été desservis une fois chacun. Le car termine loin de l'école : c'est permis ici, mais pas à la question 3.}\par\addvspace{0.4em}
\end{document}
