\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 76}

\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=76}\\[2pt]
    {\small\ttfamily\bfseries\color{red} HAMI0076}
\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=0.7745, line join=round, line cap=round]
\draw[line width=0.5pt] (1.389,11.488) -- (1.667,11.411) -- (1.948,11.341) -- (2.23,11.277) -- (2.514,11.22) -- (2.799,11.169) -- (3.085,11.126) -- (3.372,11.089) -- (3.659,11.058) -- (3.948,11.035) -- (4.237,11.018) -- (4.526,11.008) -- (4.815,11.005) -- (5.104,11.009) -- (5.393,11.02);
\draw[line width=0.5pt] (1.389,11.488) -- (1.426,11.226) -- (1.458,10.964) -- (1.483,10.7) -- (1.502,10.436) -- (1.514,10.172) -- (1.521,9.907) -- (1.521,9.642) -- (1.515,9.378) -- (1.503,9.113) -- (1.485,8.849) -- (1.46,8.586) -- (1.429,8.323) -- (1.392,8.061) -- (1.349,7.8);
\draw[line width=0.5pt] (5.393,11.02) -- (5.599,10.969) -- (5.807,10.924) -- (6.016,10.883) -- (6.225,10.848) -- (6.435,10.817) -- (6.647,10.792) -- (6.858,10.771) -- (7.07,10.755) -- (7.283,10.744) -- (7.495,10.738) -- (7.708,10.738) -- (7.92,10.742) -- (8.132,10.751) -- (8.344,10.765);
\draw[line width=0.5pt] (5.393,11.02) -- (5.387,10.794) -- (5.376,10.568) -- (5.36,10.343) -- (5.338,10.118) -- (5.311,9.894) -- (5.279,9.67) -- (5.242,9.447) -- (5.199,9.226) -- (5.151,9.005) -- (5.098,8.785) -- (5.04,8.567) -- (4.976,8.35) -- (4.908,8.135) -- (4.834,7.921);
\draw[line width=0.5pt] (8.344,10.765) -- (8.298,10.576) -- (8.255,10.385) -- (8.217,10.194) -- (8.184,10.001) -- (8.155,9.808) -- (8.131,9.614) -- (8.112,9.42) -- (8.097,9.225) -- (8.086,9.03) -- (8.08,8.835) -- (8.079,8.64) -- (8.082,8.444) -- (8.09,8.249) -- (8.103,8.055);
\draw[line width=0.5pt] (8.103,8.055) -- (8.118,7.859) -- (8.129,7.664) -- (8.135,7.468) -- (8.137,7.272) -- (8.134,7.075) -- (8.127,6.879) -- (8.114,6.684) -- (8.098,6.488) -- (8.076,6.293) -- (8.05,6.099) -- (8.02,5.905) -- (7.985,5.712) -- (7.945,5.52) -- (7.901,5.329);
\draw[line width=0.5pt] (4.834,7.921) -- (5.067,7.895) -- (5.301,7.874) -- (5.535,7.859) -- (5.77,7.849) -- (6.005,7.845) -- (6.239,7.846) -- (6.474,7.853) -- (6.708,7.865) -- (6.943,7.883) -- (7.176,7.907) -- (7.409,7.935) -- (7.641,7.97) -- (7.872,8.009) -- (8.103,8.055);
\draw[line width=0.5pt] (4.834,7.921) -- (4.858,7.718) -- (4.877,7.514) -- (4.891,7.31) -- (4.9,7.105) -- (4.905,6.9) -- (4.905,6.695) -- (4.899,6.49) -- (4.889,6.285) -- (4.875,6.081) -- (4.855,5.877) -- (4.831,5.673) -- (4.802,5.471) -- (4.768,5.269) -- (4.729,5.067);
\draw[line width=0.5pt] (1.349,7.8) -- (1.39,7.624) -- (1.435,7.449) -- (1.485,7.276) -- (1.538,7.103) -- (1.596,6.932) -- (1.657,6.762) -- (1.723,6.594) -- (1.792,6.427) -- (1.865,6.262) -- (1.943,6.098) -- (2.024,5.937) -- (2.108,5.777) -- (2.197,5.62) -- (2.289,5.465);
\draw[line width=0.5pt] (2.289,5.465) -- (2.466,5.463) -- (2.643,5.458) -- (2.82,5.448) -- (2.997,5.434) -- (3.174,5.416) -- (3.35,5.393) -- (3.525,5.367) -- (3.7,5.336) -- (3.874,5.302) -- (4.047,5.263) -- (4.219,5.22) -- (4.39,5.173) -- (4.56,5.122) -- (4.729,5.067);
\draw[line width=0.5pt] (2.289,5.465) -- (2.235,5.185) -- (2.187,4.903) -- (2.146,4.621) -- (2.112,4.337) -- (2.084,4.053) -- (2.063,3.768) -- (2.049,3.483) -- (2.042,3.197) -- (2.041,2.911) -- (2.047,2.626) -- (2.059,2.341) -- (2.079,2.056) -- (2.105,1.771) -- (2.137,1.488);
\draw[line width=0.5pt] (7.901,5.329) -- (7.975,5.081) -- (8.043,4.83) -- (8.104,4.578) -- (8.16,4.324) -- (8.21,4.069) -- (8.253,3.813) -- (8.291,3.556) -- (8.323,3.298) -- (8.349,3.04) -- (8.368,2.781) -- (8.382,2.522) -- (8.389,2.262) -- (8.39,2.003) -- (8.385,1.743);
\draw[line width=0.5pt] (4.729,5.067) -- (4.957,5.051) -- (5.185,5.041) -- (5.413,5.035) -- (5.641,5.035) -- (5.87,5.041) -- (6.098,5.051) -- (6.326,5.068) -- (6.553,5.089) -- (6.78,5.116) -- (7.007,5.148) -- (7.232,5.185) -- (7.456,5.228) -- (7.679,5.276) -- (7.901,5.329);
\draw[line width=0.5pt] (4.729,5.067) -- (4.799,4.844) -- (4.864,4.619) -- (4.924,4.393) -- (4.978,4.165) -- (5.027,3.935) -- (5.07,3.705) -- (5.109,3.474) -- (5.141,3.242) -- (5.168,3.009) -- (5.19,2.776) -- (5.206,2.542) -- (5.217,2.308) -- (5.222,2.074) -- (5.222,1.84);
\draw[line width=0.5pt] (5.222,1.84) -- (5.445,1.798) -- (5.669,1.762) -- (5.894,1.731) -- (6.12,1.706) -- (6.346,1.685) -- (6.573,1.671) -- (6.8,1.661) -- (7.027,1.657) -- (7.254,1.658) -- (7.481,1.664) -- (7.708,1.676) -- (7.934,1.693) -- (8.16,1.715) -- (8.385,1.743);
\draw[line width=0.5pt] (2.137,1.488) -- (2.352,1.547) -- (2.568,1.6) -- (2.786,1.649) -- (3.004,1.692) -- (3.224,1.73) -- (3.444,1.763) -- (3.665,1.791) -- (3.887,1.814) -- (4.109,1.831) -- (4.332,1.843) -- (4.554,1.85) -- (4.777,1.852) -- (5.0,1.848) -- (5.222,1.84);
\filldraw[fill=red!16, draw=black, line width=0.5pt] (1.549,11.488) -- (1.527,11.568) -- (1.469,11.627) -- (1.389,11.648) -- (1.309,11.627) -- (1.25,11.568) -- (1.229,11.488) -- (1.25,11.408) -- (1.309,11.349) -- (1.389,11.328) -- (1.469,11.349) -- (1.527,11.408) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (5.553,11.02) -- (5.532,11.1) -- (5.473,11.158) -- (5.393,11.18) -- (5.313,11.158) -- (5.254,11.1) -- (5.233,11.02) -- (5.254,10.94) -- (5.313,10.881) -- (5.393,10.86) -- (5.473,10.881) -- (5.532,10.94) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (8.504,10.765) -- (8.483,10.845) -- (8.424,10.904) -- (8.344,10.925) -- (8.264,10.904) -- (8.206,10.845) -- (8.184,10.765) -- (8.206,10.685) -- (8.264,10.627) -- (8.344,10.605) -- (8.424,10.627) -- (8.483,10.685) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (8.263,8.055) -- (8.241,8.135) -- (8.183,8.193) -- (8.103,8.215) -- (8.023,8.193) -- (7.964,8.135) -- (7.943,8.055) -- (7.964,7.975) -- (8.023,7.916) -- (8.103,7.895) -- (8.183,7.916) -- (8.241,7.975) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (4.994,7.921) -- (4.973,8.001) -- (4.914,8.06) -- (4.834,8.081) -- (4.754,8.06) -- (4.696,8.001) -- (4.674,7.921) -- (4.696,7.841) -- (4.754,7.783) -- (4.834,7.761) -- (4.914,7.783) -- (4.973,7.841) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (1.509,7.8) -- (1.488,7.88) -- (1.429,7.939) -- (1.349,7.96) -- (1.269,7.939) -- (1.211,7.88) -- (1.189,7.8) -- (1.211,7.72) -- (1.269,7.661) -- (1.349,7.64) -- (1.429,7.661) -- (1.488,7.72) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (2.449,5.465) -- (2.427,5.545) -- (2.369,5.603) -- (2.289,5.625) -- (2.209,5.603) -- (2.15,5.545) -- (2.129,5.465) -- (2.15,5.385) -- (2.209,5.326) -- (2.289,5.305) -- (2.369,5.326) -- (2.427,5.385) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (8.061,5.329) -- (8.04,5.409) -- (7.981,5.468) -- (7.901,5.489) -- (7.821,5.468) -- (7.763,5.409) -- (7.741,5.329) -- (7.763,5.249) -- (7.821,5.191) -- (7.901,5.169) -- (7.981,5.191) -- (8.04,5.249) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (4.889,5.067) -- (4.867,5.147) -- (4.809,5.206) -- (4.729,5.227) -- (4.649,5.206) -- (4.59,5.147) -- (4.569,5.067) -- (4.59,4.987) -- (4.649,4.929) -- (4.729,4.907) -- (4.809,4.929) -- (4.867,4.987) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (5.382,1.84) -- (5.36,1.92) -- (5.302,1.978) -- (5.222,2.0) -- (5.142,1.978) -- (5.083,1.92) -- (5.062,1.84) -- (5.083,1.76) -- (5.142,1.701) -- (5.222,1.68) -- (5.302,1.701) -- (5.36,1.76) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (8.545,1.743) -- (8.524,1.823) -- (8.465,1.882) -- (8.385,1.903) -- (8.305,1.882) -- (8.247,1.823) -- (8.225,1.743) -- (8.247,1.663) -- (8.305,1.605) -- (8.385,1.583) -- (8.465,1.605) -- (8.524,1.663) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (2.297,1.488) -- (2.276,1.568) -- (2.217,1.627) -- (2.137,1.648) -- (2.057,1.627) -- (1.999,1.568) -- (1.977,1.488) -- (1.999,1.408) -- (2.057,1.349) -- (2.137,1.328) -- (2.217,1.349) -- (2.276,1.408) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (3.417,11.086) -- (3.539,11.105) -- (3.649,11.161) -- (3.736,11.248) -- (3.792,11.358) -- (3.811,11.48) -- (3.792,11.602) -- (3.736,11.711) -- (3.649,11.799) -- (3.539,11.855) -- (3.417,11.874) -- (3.417,11.874) -- (3.296,11.855) -- (3.186,11.799) -- (3.099,11.711) -- (3.043,11.602) -- (3.023,11.48) -- (3.043,11.358) -- (3.099,11.248) -- (3.186,11.161) -- (3.296,11.105) -- (3.417,11.086) -- cycle;
\node at (3.417,11.48) {\scalebox{1.291}{\small 1}};
\filldraw[fill=white, draw=black, line width=0.5pt] (1.915,9.244) -- (2.037,9.264) -- (2.147,9.319) -- (2.234,9.407) -- (2.29,9.516) -- (2.309,9.638) -- (2.29,9.76) -- (2.234,9.87) -- (2.147,9.957) -- (2.037,10.013) -- (1.915,10.032) -- (1.915,10.032) -- (1.793,10.013) -- (1.683,9.957) -- (1.596,9.87) -- (1.54,9.76) -- (1.521,9.638) -- (1.54,9.516) -- (1.596,9.407) -- (1.683,9.319) -- (1.793,9.264) -- (1.915,9.244) -- cycle;
\node at (1.915,9.638) {\scalebox{1.291}{\small 2}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.892,10.769) -- (7.014,10.789) -- (7.124,10.845) -- (7.211,10.932) -- (7.267,11.042) -- (7.286,11.163) -- (7.267,11.285) -- (7.211,11.395) -- (7.124,11.482) -- (7.014,11.538) -- (6.892,11.557) -- (6.892,11.557) -- (6.77,11.538) -- (6.66,11.482) -- (6.573,11.395) -- (6.517,11.285) -- (6.498,11.163) -- (6.517,11.042) -- (6.573,10.932) -- (6.66,10.845) -- (6.77,10.789) -- (6.892,10.769) -- cycle;
\node at (6.892,11.163) {\scalebox{1.291}{\small 3}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.629,8.984) -- (5.751,9.003) -- (5.861,9.059) -- (5.948,9.146) -- (6.004,9.256) -- (6.023,9.378) -- (6.004,9.499) -- (5.948,9.609) -- (5.861,9.696) -- (5.751,9.752) -- (5.629,9.771) -- (5.629,9.771) -- (5.507,9.752) -- (5.398,9.696) -- (5.311,9.609) -- (5.255,9.499) -- (5.235,9.378) -- (5.255,9.256) -- (5.311,9.146) -- (5.398,9.059) -- (5.507,9.003) -- (5.629,8.984) -- cycle;
\node at (5.629,9.378) {\scalebox{1.291}{\small 4}};
\filldraw[fill=white, draw=black, line width=0.5pt] (8.504,8.991) -- (8.626,9.01) -- (8.736,9.066) -- (8.823,9.153) -- (8.879,9.263) -- (8.898,9.385) -- (8.879,9.507) -- (8.823,9.617) -- (8.736,9.704) -- (8.626,9.76) -- (8.504,9.779) -- (8.504,9.779) -- (8.382,9.76) -- (8.272,9.704) -- (8.185,9.617) -- (8.129,9.507) -- (8.11,9.385) -- (8.129,9.263) -- (8.185,9.153) -- (8.272,9.066) -- (8.382,9.01) -- (8.504,8.991) -- cycle;
\node at (8.504,9.385) {\scalebox{1.291}{\small 5}};
\filldraw[fill=white, draw=black, line width=0.5pt] (8.507,6.261) -- (8.629,6.28) -- (8.739,6.336) -- (8.826,6.423) -- (8.882,6.533) -- (8.901,6.655) -- (8.882,6.776) -- (8.826,6.886) -- (8.739,6.973) -- (8.629,7.029) -- (8.507,7.049) -- (8.507,7.049) -- (8.386,7.029) -- (8.276,6.973) -- (8.189,6.886) -- (8.133,6.776) -- (8.113,6.655) -- (8.133,6.533) -- (8.189,6.423) -- (8.276,6.336) -- (8.386,6.28) -- (8.507,6.261) -- cycle;
\node at (8.507,6.655) {\scalebox{1.291}{\small 6}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.458,7.853) -- (6.58,7.872) -- (6.689,7.928) -- (6.777,8.015) -- (6.833,8.125) -- (6.852,8.247) -- (6.833,8.368) -- (6.777,8.478) -- (6.689,8.565) -- (6.58,8.621) -- (6.458,8.641) -- (6.458,8.641) -- (6.336,8.621) -- (6.226,8.565) -- (6.139,8.478) -- (6.083,8.368) -- (6.064,8.247) -- (6.083,8.125) -- (6.139,8.015) -- (6.226,7.928) -- (6.336,7.872) -- (6.458,7.853) -- cycle;
\node at (6.458,8.247) {\scalebox{1.291}{\small 7}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.293,6.082) -- (5.415,6.101) -- (5.525,6.157) -- (5.612,6.244) -- (5.668,6.354) -- (5.687,6.475) -- (5.668,6.597) -- (5.612,6.707) -- (5.525,6.794) -- (5.415,6.85) -- (5.293,6.869) -- (5.293,6.869) -- (5.171,6.85) -- (5.061,6.794) -- (4.974,6.707) -- (4.918,6.597) -- (4.899,6.475) -- (4.918,6.354) -- (4.974,6.244) -- (5.061,6.157) -- (5.171,6.101) -- (5.293,6.082) -- cycle;
\node at (5.293,6.475) {\scalebox{1.291}{\small 8}};
\filldraw[fill=white, draw=black, line width=0.5pt] (2.088,6.347) -- (2.21,6.366) -- (2.32,6.422) -- (2.407,6.509) -- (2.463,6.619) -- (2.482,6.741) -- (2.463,6.862) -- (2.407,6.972) -- (2.32,7.059) -- (2.21,7.115) -- (2.088,7.135) -- (2.088,7.135) -- (1.966,7.115) -- (1.857,7.059) -- (1.769,6.972) -- (1.713,6.862) -- (1.694,6.741) -- (1.713,6.619) -- (1.769,6.509) -- (1.857,6.422) -- (1.966,6.366) -- (2.088,6.347) -- cycle;
\node at (2.088,6.741) {\scalebox{1.291}{\small 9}};
\filldraw[fill=white, draw=black, line width=0.5pt] (3.774,5.362) -- (3.896,5.381) -- (4.005,5.437) -- (4.093,5.524) -- (4.149,5.634) -- (4.168,5.756) -- (4.149,5.877) -- (4.093,5.987) -- (4.005,6.074) -- (3.896,6.13) -- (3.774,6.149) -- (3.403,6.149) -- (3.282,6.13) -- (3.172,6.074) -- (3.085,5.987) -- (3.029,5.877) -- (3.009,5.756) -- (3.029,5.634) -- (3.085,5.524) -- (3.172,5.437) -- (3.282,5.381) -- (3.403,5.362) -- cycle;
\node at (3.589,5.756) {\scalebox{1.291}{\small 10}};
\filldraw[fill=white, draw=black, line width=0.5pt] (2.628,3.074) -- (2.75,3.093) -- (2.86,3.149) -- (2.947,3.236) -- (3.003,3.346) -- (3.022,3.468) -- (3.003,3.589) -- (2.947,3.699) -- (2.86,3.786) -- (2.75,3.842) -- (2.628,3.862) -- (2.257,3.862) -- (2.136,3.842) -- (2.026,3.786) -- (1.939,3.699) -- (1.883,3.589) -- (1.863,3.468) -- (1.883,3.346) -- (1.939,3.236) -- (2.026,3.149) -- (2.136,3.093) -- (2.257,3.074) -- cycle;
\node at (2.443,3.468) {\scalebox{1.291}{\small 11}};
\filldraw[fill=white, draw=black, line width=0.5pt] (8.867,3.215) -- (8.989,3.234) -- (9.098,3.29) -- (9.186,3.377) -- (9.242,3.487) -- (9.261,3.609) -- (9.242,3.731) -- (9.186,3.84) -- (9.098,3.928) -- (8.989,3.984) -- (8.867,4.003) -- (8.496,4.003) -- (8.374,3.984) -- (8.265,3.928) -- (8.178,3.84) -- (8.122,3.731) -- (8.102,3.609) -- (8.122,3.487) -- (8.178,3.377) -- (8.265,3.29) -- (8.374,3.234) -- (8.496,3.215) -- cycle;
\node at (8.682,3.609) {\scalebox{1.291}{\small 12}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.479,5.066) -- (6.601,5.085) -- (6.71,5.141) -- (6.798,5.229) -- (6.854,5.338) -- (6.873,5.46) -- (6.854,5.582) -- (6.798,5.692) -- (6.71,5.779) -- (6.601,5.835) -- (6.479,5.854) -- (6.108,5.854) -- (5.986,5.835) -- (5.877,5.779) -- (5.789,5.692) -- (5.734,5.582) -- (5.714,5.46) -- (5.734,5.338) -- (5.789,5.229) -- (5.877,5.141) -- (5.986,5.085) -- (6.108,5.066) -- cycle;
\node at (6.294,5.46) {\scalebox{1.291}{\small 13}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.683,3.139) -- (5.805,3.159) -- (5.915,3.215) -- (6.002,3.302) -- (6.058,3.412) -- (6.077,3.533) -- (6.058,3.655) -- (6.002,3.765) -- (5.915,3.852) -- (5.805,3.908) -- (5.683,3.927) -- (5.313,3.927) -- (5.191,3.908) -- (5.081,3.852) -- (4.994,3.765) -- (4.938,3.655) -- (4.919,3.533) -- (4.938,3.412) -- (4.994,3.302) -- (5.081,3.215) -- (5.191,3.159) -- (5.313,3.139) -- cycle;
\node at (5.498,3.533) {\scalebox{1.291}{\small 14}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.997,1.661) -- (7.119,1.68) -- (7.228,1.736) -- (7.316,1.823) -- (7.372,1.933) -- (7.391,2.055) -- (7.372,2.176) -- (7.316,2.286) -- (7.228,2.373) -- (7.119,2.429) -- (6.997,2.449) -- (6.626,2.449) -- (6.504,2.429) -- (6.395,2.373) -- (6.308,2.286) -- (6.252,2.176) -- (6.232,2.055) -- (6.252,1.933) -- (6.308,1.823) -- (6.395,1.736) -- (6.504,1.68) -- (6.626,1.661) -- cycle;
\node at (6.812,2.055) {\scalebox{1.291}{\small 15}};
\filldraw[fill=white, draw=black, line width=0.5pt] (3.806,1.789) -- (3.928,1.808) -- (4.037,1.864) -- (4.125,1.951) -- (4.181,2.061) -- (4.2,2.182) -- (4.181,2.304) -- (4.125,2.414) -- (4.037,2.501) -- (3.928,2.557) -- (3.806,2.576) -- (3.435,2.576) -- (3.313,2.557) -- (3.204,2.501) -- (3.117,2.414) -- (3.061,2.304) -- (3.041,2.182) -- (3.061,2.061) -- (3.117,1.951) -- (3.204,1.864) -- (3.313,1.808) -- (3.435,1.789) -- cycle;
\node at (3.621,2.182) {\scalebox{1.291}{\small 16}};
\filldraw[fill=yellow!35, draw=black, line width=0.5pt] (5.093,10.72) -- (5.693,10.72) -- (5.693,11.32) -- (5.093,11.32) -- cycle;
\node at (5.393,11.02) {\scalebox{1.291}{\small a}};
\filldraw[fill=green!18, draw=black, line width=0.5pt] (1.16,2.475) -- (1.76,2.475) -- (1.76,3.075) -- (1.16,3.075) -- cycle;
\node at (1.46,2.775) {\scalebox{1.291}{\small b}};
\filldraw[fill=red!16, draw=black, line width=0.5pt] (2.391,0.967) -- (2.991,0.967) -- (2.991,1.567) -- (2.391,1.567) -- cycle;
\node at (2.691,1.267) {\scalebox{1.291}{\small c}};
\filldraw[fill=green!18, draw=black, line width=0.5pt] (6.222,9.068) -- (6.822,9.068) -- (6.822,9.668) -- (6.222,9.668) -- cycle;
\node at (6.522,9.368) {\scalebox{1.291}{\small d}};
\node at (1.025,11.99) {\scalebox{1.291}{\small A}};
\node at (5.446,11.637) {\scalebox{1.291}{\small B}};
\node at (8.726,11.254) {\scalebox{1.291}{\small C}};
\node at (8.657,8.333) {\scalebox{1.291}{\small D}};
\node at (4.76,8.537) {\scalebox{1.291}{\small E}};
\node at (0.765,8.008) {\scalebox{1.291}{\small F}};
\node at (1.709,5.244) {\scalebox{1.291}{\small G}};
\node at (8.476,5.097) {\scalebox{1.291}{\small H}};
\node at (4.611,4.459) {\scalebox{1.291}{\small I}};
\node at (5.251,1.22) {\scalebox{1.291}{\small J}};
\node at (8.744,1.238) {\scalebox{1.291}{\small K}};
\node at (1.829,0.95) {\scalebox{1.291}{\small L}};
\draw[line width=0.5pt] (9.685,10.538) -- (9.685,11.638);
\draw[line width=0.5pt] (9.454,11.253) -- (9.685,11.638) -- (9.916,11.253);
\draw[line width=0.5pt] (9.383,11.088) -- (9.988,11.088);
\node at (9.685,12.023) {\scalebox{1.291}{\small N}};
\end{tikzpicture}
\end{center}
\noindent \textbf{Le car part de l'école, au carrefour B, 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 & ⑨ rue Verte & Ⓐ Place du Marché & Ⓙ Rond-point du Pont \\ \hline
① chemin de Ronde & ⑩ boulevard du Parc & Ⓑ Rond-point de la Gare & Ⓚ Place des Tanneurs \\ \hline
② rue des Jardins & ⑪ rue Basse & Ⓒ Place du Vieux-Puits & Ⓛ Place de l'Église \\ \hline
③ allée des Tilleuls & ⑫ rue du Stade & Ⓓ Rond-point de la Poste & \cellcolor{black!32}\bfseries Les bâtiments \\ \hline
④ rue de la Mairie & ⑬ venelle du Chat & Ⓔ Carrefour des Tilleuls & \textbf{a} l'école \\ \hline
⑤ rue Haute & ⑭ rue des Lilas & Ⓕ Place de la Fontaine & \textbf{b} la bibliothèque \\ \hline
⑥ chemin Creux & ⑮ quai aux Fleurs & Ⓖ Rond-point du Stade & \textbf{c} le lavoir \\ \hline
⑦ avenue de la Gare & ⑯ rue Pasteur & Ⓗ Carrefour du Moulin & \textbf{d} la mairie \\ \hline
⑧ rue Neuve & \cellcolor{black!32}\bfseries Les carrefours & Ⓘ Carrefour de la Mairie &  \\ \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=0.7934, line join=round, line cap=round]
\draw[line width=0.5pt] (1.389,11.488) -- (1.667,11.411) -- (1.948,11.341) -- (2.23,11.277) -- (2.514,11.22) -- (2.799,11.169) -- (3.085,11.126) -- (3.372,11.089) -- (3.659,11.058) -- (3.948,11.035) -- (4.237,11.018) -- (4.526,11.008) -- (4.815,11.005) -- (5.104,11.009) -- (5.393,11.02);
\draw[line width=0.5pt] (1.389,11.488) -- (1.426,11.226) -- (1.458,10.964) -- (1.483,10.7) -- (1.502,10.436) -- (1.514,10.172) -- (1.521,9.907) -- (1.521,9.642) -- (1.515,9.378) -- (1.503,9.113) -- (1.485,8.849) -- (1.46,8.586) -- (1.429,8.323) -- (1.392,8.061) -- (1.349,7.8);
\draw[line width=0.5pt] (5.393,11.02) -- (5.599,10.969) -- (5.807,10.924) -- (6.016,10.883) -- (6.225,10.848) -- (6.435,10.817) -- (6.647,10.792) -- (6.858,10.771) -- (7.07,10.755) -- (7.283,10.744) -- (7.495,10.738) -- (7.708,10.738) -- (7.92,10.742) -- (8.132,10.751) -- (8.344,10.765);
\draw[line width=0.5pt] (5.393,11.02) -- (5.387,10.794) -- (5.376,10.568) -- (5.36,10.343) -- (5.338,10.118) -- (5.311,9.894) -- (5.279,9.67) -- (5.242,9.447) -- (5.199,9.226) -- (5.151,9.005) -- (5.098,8.785) -- (5.04,8.567) -- (4.976,8.35) -- (4.908,8.135) -- (4.834,7.921);
\draw[line width=0.5pt] (8.344,10.765) -- (8.298,10.576) -- (8.255,10.385) -- (8.217,10.194) -- (8.184,10.001) -- (8.155,9.808) -- (8.131,9.614) -- (8.112,9.42) -- (8.097,9.225) -- (8.086,9.03) -- (8.08,8.835) -- (8.079,8.64) -- (8.082,8.444) -- (8.09,8.249) -- (8.103,8.055);
\draw[line width=0.5pt] (8.103,8.055) -- (8.118,7.859) -- (8.129,7.664) -- (8.135,7.468) -- (8.137,7.272) -- (8.134,7.075) -- (8.127,6.879) -- (8.114,6.684) -- (8.098,6.488) -- (8.076,6.293) -- (8.05,6.099) -- (8.02,5.905) -- (7.985,5.712) -- (7.945,5.52) -- (7.901,5.329);
\draw[line width=0.5pt] (4.834,7.921) -- (5.067,7.895) -- (5.301,7.874) -- (5.535,7.859) -- (5.77,7.849) -- (6.005,7.845) -- (6.239,7.846) -- (6.474,7.853) -- (6.708,7.865) -- (6.943,7.883) -- (7.176,7.907) -- (7.409,7.935) -- (7.641,7.97) -- (7.872,8.009) -- (8.103,8.055);
\draw[line width=0.5pt] (4.834,7.921) -- (4.858,7.718) -- (4.877,7.514) -- (4.891,7.31) -- (4.9,7.105) -- (4.905,6.9) -- (4.905,6.695) -- (4.899,6.49) -- (4.889,6.285) -- (4.875,6.081) -- (4.855,5.877) -- (4.831,5.673) -- (4.802,5.471) -- (4.768,5.269) -- (4.729,5.067);
\draw[line width=0.5pt] (1.349,7.8) -- (1.39,7.624) -- (1.435,7.449) -- (1.485,7.276) -- (1.538,7.103) -- (1.596,6.932) -- (1.657,6.762) -- (1.723,6.594) -- (1.792,6.427) -- (1.865,6.262) -- (1.943,6.098) -- (2.024,5.937) -- (2.108,5.777) -- (2.197,5.62) -- (2.289,5.465);
\draw[line width=0.5pt] (2.289,5.465) -- (2.466,5.463) -- (2.643,5.458) -- (2.82,5.448) -- (2.997,5.434) -- (3.174,5.416) -- (3.35,5.393) -- (3.525,5.367) -- (3.7,5.336) -- (3.874,5.302) -- (4.047,5.263) -- (4.219,5.22) -- (4.39,5.173) -- (4.56,5.122) -- (4.729,5.067);
\draw[line width=0.5pt] (2.289,5.465) -- (2.235,5.185) -- (2.187,4.903) -- (2.146,4.621) -- (2.112,4.337) -- (2.084,4.053) -- (2.063,3.768) -- (2.049,3.483) -- (2.042,3.197) -- (2.041,2.911) -- (2.047,2.626) -- (2.059,2.341) -- (2.079,2.056) -- (2.105,1.771) -- (2.137,1.488);
\draw[line width=0.5pt] (7.901,5.329) -- (7.975,5.081) -- (8.043,4.83) -- (8.104,4.578) -- (8.16,4.324) -- (8.21,4.069) -- (8.253,3.813) -- (8.291,3.556) -- (8.323,3.298) -- (8.349,3.04) -- (8.368,2.781) -- (8.382,2.522) -- (8.389,2.262) -- (8.39,2.003) -- (8.385,1.743);
\draw[line width=0.5pt] (4.729,5.067) -- (4.957,5.051) -- (5.185,5.041) -- (5.413,5.035) -- (5.641,5.035) -- (5.87,5.041) -- (6.098,5.051) -- (6.326,5.068) -- (6.553,5.089) -- (6.78,5.116) -- (7.007,5.148) -- (7.232,5.185) -- (7.456,5.228) -- (7.679,5.276) -- (7.901,5.329);
\draw[line width=0.5pt] (4.729,5.067) -- (4.799,4.844) -- (4.864,4.619) -- (4.924,4.393) -- (4.978,4.165) -- (5.027,3.935) -- (5.07,3.705) -- (5.109,3.474) -- (5.141,3.242) -- (5.168,3.009) -- (5.19,2.776) -- (5.206,2.542) -- (5.217,2.308) -- (5.222,2.074) -- (5.222,1.84);
\draw[line width=0.5pt] (5.222,1.84) -- (5.445,1.798) -- (5.669,1.762) -- (5.894,1.731) -- (6.12,1.706) -- (6.346,1.685) -- (6.573,1.671) -- (6.8,1.661) -- (7.027,1.657) -- (7.254,1.658) -- (7.481,1.664) -- (7.708,1.676) -- (7.934,1.693) -- (8.16,1.715) -- (8.385,1.743);
\draw[line width=0.5pt] (2.137,1.488) -- (2.352,1.547) -- (2.568,1.6) -- (2.786,1.649) -- (3.004,1.692) -- (3.224,1.73) -- (3.444,1.763) -- (3.665,1.791) -- (3.887,1.814) -- (4.109,1.831) -- (4.332,1.843) -- (4.554,1.85) -- (4.777,1.852) -- (5.0,1.848) -- (5.222,1.84);
\filldraw[fill=white, draw=black, line width=0.5pt] (1.762,11.488) -- (1.734,11.631) -- (1.653,11.752) -- (1.532,11.833) -- (1.389,11.861) -- (1.246,11.833) -- (1.125,11.752) -- (1.044,11.631) -- (1.016,11.488) -- (1.044,11.345) -- (1.125,11.224) -- (1.246,11.143) -- (1.389,11.115) -- (1.532,11.143) -- (1.653,11.224) -- (1.734,11.345) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (5.766,11.02) -- (5.738,11.162) -- (5.657,11.284) -- (5.536,11.364) -- (5.393,11.393) -- (5.25,11.364) -- (5.129,11.284) -- (5.048,11.162) -- (5.02,11.02) -- (5.048,10.877) -- (5.129,10.756) -- (5.25,10.675) -- (5.393,10.646) -- (5.536,10.675) -- (5.657,10.756) -- (5.738,10.877) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (8.718,10.765) -- (8.689,10.908) -- (8.608,11.029) -- (8.487,11.11) -- (8.344,11.139) -- (8.202,11.11) -- (8.08,11.029) -- (8.0,10.908) -- (7.971,10.765) -- (8.0,10.623) -- (8.08,10.502) -- (8.202,10.421) -- (8.344,10.392) -- (8.487,10.421) -- (8.608,10.502) -- (8.689,10.623) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (8.476,8.055) -- (8.447,8.197) -- (8.366,8.319) -- (8.245,8.399) -- (8.103,8.428) -- (7.96,8.399) -- (7.839,8.319) -- (7.758,8.197) -- (7.729,8.055) -- (7.758,7.912) -- (7.839,7.791) -- (7.96,7.71) -- (8.103,7.681) -- (8.245,7.71) -- (8.366,7.791) -- (8.447,7.912) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (5.208,7.921) -- (5.179,8.064) -- (5.098,8.185) -- (4.977,8.266) -- (4.834,8.295) -- (4.692,8.266) -- (4.571,8.185) -- (4.49,8.064) -- (4.461,7.921) -- (4.49,7.778) -- (4.571,7.657) -- (4.692,7.576) -- (4.834,7.548) -- (4.977,7.576) -- (5.098,7.657) -- (5.179,7.778) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (1.722,7.8) -- (1.694,7.943) -- (1.613,8.064) -- (1.492,8.145) -- (1.349,8.173) -- (1.206,8.145) -- (1.085,8.064) -- (1.004,7.943) -- (0.976,7.8) -- (1.004,7.657) -- (1.085,7.536) -- (1.206,7.455) -- (1.349,7.427) -- (1.492,7.455) -- (1.613,7.536) -- (1.694,7.657) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (2.662,5.465) -- (2.634,5.608) -- (2.553,5.729) -- (2.432,5.81) -- (2.289,5.838) -- (2.146,5.81) -- (2.025,5.729) -- (1.944,5.608) -- (1.916,5.465) -- (1.944,5.322) -- (2.025,5.201) -- (2.146,5.12) -- (2.289,5.092) -- (2.432,5.12) -- (2.553,5.201) -- (2.634,5.322) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (8.275,5.329) -- (8.246,5.472) -- (8.165,5.593) -- (8.044,5.674) -- (7.901,5.703) -- (7.759,5.674) -- (7.638,5.593) -- (7.557,5.472) -- (7.528,5.329) -- (7.557,5.187) -- (7.638,5.065) -- (7.759,4.985) -- (7.901,4.956) -- (8.044,4.985) -- (8.165,5.065) -- (8.246,5.187) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (5.102,5.067) -- (5.074,5.21) -- (4.993,5.331) -- (4.872,5.412) -- (4.729,5.441) -- (4.586,5.412) -- (4.465,5.331) -- (4.384,5.21) -- (4.356,5.067) -- (4.384,4.925) -- (4.465,4.804) -- (4.586,4.723) -- (4.729,4.694) -- (4.872,4.723) -- (4.993,4.804) -- (5.074,4.925) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (5.595,1.84) -- (5.567,1.982) -- (5.486,2.104) -- (5.365,2.184) -- (5.222,2.213) -- (5.079,2.184) -- (4.958,2.104) -- (4.877,1.982) -- (4.849,1.84) -- (4.877,1.697) -- (4.958,1.576) -- (5.079,1.495) -- (5.222,1.466) -- (5.365,1.495) -- (5.486,1.576) -- (5.567,1.697) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (8.758,1.743) -- (8.73,1.886) -- (8.649,2.007) -- (8.528,2.088) -- (8.385,2.116) -- (8.242,2.088) -- (8.121,2.007) -- (8.04,1.886) -- (8.012,1.743) -- (8.04,1.6) -- (8.121,1.479) -- (8.242,1.398) -- (8.385,1.37) -- (8.528,1.398) -- (8.649,1.479) -- (8.73,1.6) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (2.511,1.488) -- (2.482,1.631) -- (2.401,1.752) -- (2.28,1.833) -- (2.137,1.861) -- (1.995,1.833) -- (1.874,1.752) -- (1.793,1.631) -- (1.764,1.488) -- (1.793,1.345) -- (1.874,1.224) -- (1.995,1.143) -- (2.137,1.115) -- (2.28,1.143) -- (2.401,1.224) -- (2.482,1.345) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (3.416,11.086) -- (3.535,11.105) -- (3.642,11.16) -- (3.727,11.245) -- (3.782,11.352) -- (3.801,11.471) -- (3.782,11.589) -- (3.727,11.697) -- (3.642,11.782) -- (3.535,11.836) -- (3.416,11.855) -- (3.416,11.855) -- (3.297,11.836) -- (3.19,11.782) -- (3.105,11.697) -- (3.051,11.589) -- (3.032,11.471) -- (3.051,11.352) -- (3.105,11.245) -- (3.19,11.16) -- (3.297,11.105) -- (3.416,11.086) -- cycle;
\node at (3.416,11.471) {\scalebox{1.26}{\small 1}};
\filldraw[fill=white, draw=black, line width=0.5pt] (1.906,9.254) -- (2.024,9.273) -- (2.132,9.327) -- (2.217,9.412) -- (2.271,9.519) -- (2.29,9.638) -- (2.271,9.757) -- (2.217,9.864) -- (2.132,9.949) -- (2.024,10.004) -- (1.906,10.023) -- (1.906,10.023) -- (1.787,10.004) -- (1.68,9.949) -- (1.595,9.864) -- (1.54,9.757) -- (1.521,9.638) -- (1.54,9.519) -- (1.595,9.412) -- (1.68,9.327) -- (1.787,9.273) -- (1.906,9.254) -- cycle;
\node at (1.906,9.638) {\scalebox{1.26}{\small 2}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.891,10.769) -- (7.01,10.788) -- (7.117,10.843) -- (7.202,10.928) -- (7.257,11.035) -- (7.276,11.154) -- (7.257,11.273) -- (7.202,11.38) -- (7.117,11.465) -- (7.01,11.52) -- (6.891,11.538) -- (6.891,11.538) -- (6.772,11.52) -- (6.665,11.465) -- (6.58,11.38) -- (6.525,11.273) -- (6.507,11.154) -- (6.525,11.035) -- (6.58,10.928) -- (6.665,10.843) -- (6.772,10.788) -- (6.891,10.769) -- cycle;
\node at (6.891,11.154) {\scalebox{1.26}{\small 3}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.62,8.995) -- (5.739,9.014) -- (5.846,9.068) -- (5.931,9.153) -- (5.986,9.26) -- (6.004,9.379) -- (5.986,9.498) -- (5.931,9.605) -- (5.846,9.69) -- (5.739,9.745) -- (5.62,9.764) -- (5.62,9.764) -- (5.501,9.745) -- (5.394,9.69) -- (5.309,9.605) -- (5.254,9.498) -- (5.235,9.379) -- (5.254,9.26) -- (5.309,9.153) -- (5.394,9.068) -- (5.501,9.014) -- (5.62,8.995) -- cycle;
\node at (5.62,9.379) {\scalebox{1.26}{\small 4}};
\filldraw[fill=white, draw=black, line width=0.5pt] (8.495,9.001) -- (8.613,9.02) -- (8.721,9.075) -- (8.806,9.16) -- (8.86,9.267) -- (8.879,9.386) -- (8.86,9.505) -- (8.806,9.612) -- (8.721,9.697) -- (8.613,9.752) -- (8.495,9.77) -- (8.495,9.77) -- (8.376,9.752) -- (8.269,9.697) -- (8.184,9.612) -- (8.129,9.505) -- (8.11,9.386) -- (8.129,9.267) -- (8.184,9.16) -- (8.269,9.075) -- (8.376,9.02) -- (8.495,9.001) -- cycle;
\node at (8.495,9.386) {\scalebox{1.26}{\small 5}};
\filldraw[fill=white, draw=black, line width=0.5pt] (8.498,6.271) -- (8.617,6.29) -- (8.724,6.344) -- (8.809,6.429) -- (8.864,6.537) -- (8.882,6.655) -- (8.864,6.774) -- (8.809,6.881) -- (8.724,6.966) -- (8.617,7.021) -- (8.498,7.04) -- (8.498,7.04) -- (8.379,7.021) -- (8.272,6.966) -- (8.187,6.881) -- (8.132,6.774) -- (8.113,6.655) -- (8.132,6.537) -- (8.187,6.429) -- (8.272,6.344) -- (8.379,6.29) -- (8.498,6.271) -- cycle;
\node at (8.498,6.655) {\scalebox{1.26}{\small 6}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.458,7.853) -- (6.577,7.872) -- (6.684,7.926) -- (6.769,8.011) -- (6.824,8.119) -- (6.843,8.237) -- (6.824,8.356) -- (6.769,8.463) -- (6.684,8.548) -- (6.577,8.603) -- (6.458,8.622) -- (6.458,8.622) -- (6.34,8.603) -- (6.232,8.548) -- (6.147,8.463) -- (6.093,8.356) -- (6.074,8.237) -- (6.093,8.119) -- (6.147,8.011) -- (6.232,7.926) -- (6.34,7.872) -- (6.458,7.853) -- cycle;
\node at (6.458,8.237) {\scalebox{1.26}{\small 7}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.284,6.091) -- (5.402,6.11) -- (5.51,6.165) -- (5.595,6.25) -- (5.649,6.357) -- (5.668,6.476) -- (5.649,6.595) -- (5.595,6.702) -- (5.51,6.787) -- (5.402,6.841) -- (5.284,6.86) -- (5.284,6.86) -- (5.165,6.841) -- (5.058,6.787) -- (4.973,6.702) -- (4.918,6.595) -- (4.899,6.476) -- (4.918,6.357) -- (4.973,6.25) -- (5.058,6.165) -- (5.165,6.11) -- (5.284,6.091) -- cycle;
\node at (5.284,6.476) {\scalebox{1.26}{\small 8}};
\filldraw[fill=white, draw=black, line width=0.5pt] (2.079,6.353) -- (2.198,6.371) -- (2.305,6.426) -- (2.39,6.511) -- (2.445,6.618) -- (2.464,6.737) -- (2.445,6.856) -- (2.39,6.963) -- (2.305,7.048) -- (2.198,7.103) -- (2.079,7.122) -- (2.079,7.122) -- (1.961,7.103) -- (1.853,7.048) -- (1.768,6.963) -- (1.714,6.856) -- (1.695,6.737) -- (1.714,6.618) -- (1.768,6.511) -- (1.853,6.426) -- (1.961,6.371) -- (2.079,6.353) -- cycle;
\node at (2.079,6.737) {\scalebox{1.26}{\small 9}};
\filldraw[fill=white, draw=black, line width=0.5pt] (3.768,5.362) -- (3.887,5.381) -- (3.994,5.435) -- (4.079,5.52) -- (4.134,5.627) -- (4.153,5.746) -- (4.134,5.865) -- (4.079,5.972) -- (3.994,6.057) -- (3.887,6.112) -- (3.768,6.131) -- (3.406,6.131) -- (3.287,6.112) -- (3.18,6.057) -- (3.095,5.972) -- (3.04,5.865) -- (3.022,5.746) -- (3.04,5.627) -- (3.095,5.52) -- (3.18,5.435) -- (3.287,5.381) -- (3.406,5.362) -- cycle;
\node at (3.587,5.746) {\scalebox{1.26}{\small 10}};
\filldraw[fill=white, draw=black, line width=0.5pt] (2.614,3.084) -- (2.733,3.102) -- (2.84,3.157) -- (2.925,3.242) -- (2.98,3.349) -- (2.999,3.468) -- (2.98,3.587) -- (2.925,3.694) -- (2.84,3.779) -- (2.733,3.834) -- (2.614,3.853) -- (2.252,3.853) -- (2.134,3.834) -- (2.026,3.779) -- (1.941,3.694) -- (1.887,3.587) -- (1.868,3.468) -- (1.887,3.349) -- (1.941,3.242) -- (2.026,3.157) -- (2.134,3.102) -- (2.252,3.084) -- cycle;
\node at (2.433,3.468) {\scalebox{1.26}{\small 11}};
\filldraw[fill=white, draw=black, line width=0.5pt] (8.853,3.223) -- (8.972,3.242) -- (9.079,3.297) -- (9.164,3.382) -- (9.219,3.489) -- (9.238,3.608) -- (9.219,3.727) -- (9.164,3.834) -- (9.079,3.919) -- (8.972,3.973) -- (8.853,3.992) -- (8.491,3.992) -- (8.373,3.973) -- (8.265,3.919) -- (8.18,3.834) -- (8.126,3.727) -- (8.107,3.608) -- (8.126,3.489) -- (8.18,3.382) -- (8.265,3.297) -- (8.373,3.242) -- (8.491,3.223) -- cycle;
\node at (8.672,3.608) {\scalebox{1.26}{\small 12}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.475,5.066) -- (6.594,5.085) -- (6.701,5.14) -- (6.786,5.225) -- (6.841,5.332) -- (6.86,5.451) -- (6.841,5.57) -- (6.786,5.677) -- (6.701,5.762) -- (6.594,5.816) -- (6.475,5.835) -- (6.113,5.835) -- (5.995,5.816) -- (5.887,5.762) -- (5.802,5.677) -- (5.748,5.57) -- (5.729,5.451) -- (5.748,5.332) -- (5.802,5.225) -- (5.887,5.14) -- (5.995,5.085) -- (6.113,5.066) -- cycle;
\node at (6.294,5.451) {\scalebox{1.26}{\small 13}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.67,3.147) -- (5.788,3.166) -- (5.896,3.221) -- (5.981,3.306) -- (6.035,3.413) -- (6.054,3.532) -- (6.035,3.651) -- (5.981,3.758) -- (5.896,3.843) -- (5.788,3.898) -- (5.67,3.916) -- (5.308,3.916) -- (5.189,3.898) -- (5.082,3.843) -- (4.997,3.758) -- (4.942,3.651) -- (4.923,3.532) -- (4.942,3.413) -- (4.997,3.306) -- (5.082,3.221) -- (5.189,3.166) -- (5.308,3.147) -- cycle;
\node at (5.489,3.532) {\scalebox{1.26}{\small 14}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.992,1.661) -- (7.111,1.68) -- (7.218,1.734) -- (7.303,1.819) -- (7.358,1.926) -- (7.377,2.045) -- (7.358,2.164) -- (7.303,2.271) -- (7.218,2.356) -- (7.111,2.411) -- (6.992,2.43) -- (6.63,2.43) -- (6.511,2.411) -- (6.404,2.356) -- (6.319,2.271) -- (6.265,2.164) -- (6.246,2.045) -- (6.265,1.926) -- (6.319,1.819) -- (6.404,1.734) -- (6.511,1.68) -- (6.63,1.661) -- cycle;
\node at (6.811,2.045) {\scalebox{1.26}{\small 15}};
\filldraw[fill=white, draw=black, line width=0.5pt] (3.803,1.789) -- (3.921,1.807) -- (4.029,1.862) -- (4.114,1.947) -- (4.168,2.054) -- (4.187,2.173) -- (4.168,2.292) -- (4.114,2.399) -- (4.029,2.484) -- (3.921,2.539) -- (3.803,2.558) -- (3.441,2.558) -- (3.322,2.539) -- (3.215,2.484) -- (3.13,2.399) -- (3.075,2.292) -- (3.056,2.173) -- (3.075,2.054) -- (3.13,1.947) -- (3.215,1.862) -- (3.322,1.807) -- (3.441,1.789) -- cycle;
\node at (3.622,2.173) {\scalebox{1.26}{\small 16}};
\filldraw[fill=yellow!35, draw=black, line width=0.5pt] (5.093,10.72) -- (5.693,10.72) -- (5.693,11.32) -- (5.093,11.32) -- cycle;
\node at (5.393,11.02) {\scalebox{1.26}{\small a}};
\filldraw[fill=green!18, draw=black, line width=0.5pt] (1.16,2.475) -- (1.76,2.475) -- (1.76,3.075) -- (1.16,3.075) -- cycle;
\node at (1.46,2.775) {\scalebox{1.26}{\small b}};
\filldraw[fill=red!16, draw=black, line width=0.5pt] (2.391,0.967) -- (2.991,0.967) -- (2.991,1.567) -- (2.391,1.567) -- cycle;
\node at (2.691,1.267) {\scalebox{1.26}{\small c}};
\filldraw[fill=green!18, draw=black, line width=0.5pt] (6.222,9.068) -- (6.822,9.068) -- (6.822,9.668) -- (6.222,9.668) -- cycle;
\node at (6.522,9.368) {\scalebox{1.26}{\small d}};
\node at (1.025,11.99) {\scalebox{1.26}{\small A}};
\node at (5.446,11.637) {\scalebox{1.26}{\small B}};
\node at (8.726,11.254) {\scalebox{1.26}{\small C}};
\node at (8.657,8.333) {\scalebox{1.26}{\small D}};
\node at (4.76,8.537) {\scalebox{1.26}{\small E}};
\node at (0.765,8.008) {\scalebox{1.26}{\small F}};
\node at (1.709,5.244) {\scalebox{1.26}{\small G}};
\node at (8.476,5.097) {\scalebox{1.26}{\small H}};
\node at (4.611,4.459) {\scalebox{1.26}{\small I}};
\node at (5.251,1.22) {\scalebox{1.26}{\small J}};
\node at (8.744,1.238) {\scalebox{1.26}{\small K}};
\node at (1.829,0.95) {\scalebox{1.26}{\small L}};
\draw[line width=0.5pt] (9.685,10.538) -- (9.685,11.638);
\draw[line width=0.5pt] (9.454,11.253) -- (9.685,11.638) -- (9.916,11.253);
\draw[line width=0.5pt] (9.383,11.088) -- (9.988,11.088);
\node at (9.685,12.023) {\scalebox{1.26}{\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 & B, D, F, I, K, L & 6 \\ \hline
clairs & A, C, E, G, H, J & 6 \\ \hline
\end{tabular}
\end{center}
\noindent{\color{red!80!black}\bfseries Il y a \textbf{6} carrefours sombres et \textbf{6} clairs. Il y en a \textbf{autant} de chaque côté.}\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 12 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{Oui.} Un circuit existe :}\par\addvspace{0.4em}
\newpage
\noindent \textbf{Le trajet du car}\par\addvspace{0.35em}
\noindent Le car sort de l'école et prend le \textbf{chemin de Ronde ①} vers l'ouest jusqu'à Place du Marché \textbf{(A)}.\par\addvspace{0.35em}
\noindent Il tourne à gauche dans la \textbf{rue des Jardins ②}, vers le sud, jusqu'à Place de la Fontaine \textbf{(F)}.\par\addvspace{0.35em}
\noindent Il continue tout droit dans la \textbf{rue Verte ⑨}, vers le sud, jusqu'à Rond-point du Stade \textbf{(G)}.\par\addvspace{0.35em}
\noindent Il tourne à droite dans la \textbf{rue Basse ⑪}, vers le sud, jusqu'à Place de l'Église \textbf{(L)}.\par\addvspace{0.35em}
\noindent Il tourne à gauche dans la \textbf{rue Pasteur ⑯}, vers l'est, jusqu'à Rond-point du Pont \textbf{(J)}.\par\addvspace{0.35em}
\noindent Il continue tout droit dans le \textbf{quai aux Fleurs ⑮}, vers l'est, jusqu'à Place des Tanneurs \textbf{(K)}.\par\addvspace{0.35em}
\noindent Il tourne à gauche dans la \textbf{rue du Stade ⑫}, vers le nord, jusqu'à Carrefour du Moulin \textbf{(H)}.\par\addvspace{0.35em}
\noindent Il tourne à gauche dans la \textbf{venelle du Chat ⑬}, vers l'ouest, jusqu'à Carrefour de la Mairie \textbf{(I)}.\par\addvspace{0.35em}
\noindent Il tourne à droite dans la \textbf{rue Neuve ⑧}, vers le nord, jusqu'à Carrefour des Tilleuls \textbf{(E)}.\par\addvspace{0.35em}
\noindent Il tourne à droite dans l'\textbf{avenue de la Gare ⑦}, vers l'est, jusqu'à Rond-point de la Poste \textbf{(D)}.\par\addvspace{0.35em}
\noindent Il tourne à gauche dans la \textbf{rue Haute ⑤}, vers le nord, jusqu'à Place du Vieux-Puits \textbf{(C)}.\par\addvspace{0.35em}
\noindent Il tourne à gauche dans l'\textbf{allée des Tilleuls ③}, vers l'ouest, jusqu'à Rond-point de la Gare \textbf{(B)}.\par\addvspace{0.35em}
\noindent{\color{red!80!black}\bfseries Le car est passé une fois par chaque carrefour et se retrouve à l'école.}\par\addvspace{0.4em}
\noindent \textbf{4.}\par\addvspace{0.35em}
\noindent{\color{red!80!black}\bfseries \textbf{Oui}, et c'est déjà fait : le trajet ci-dessus dessert tous les carrefours. Il suffit au car de s'arrêter avant le dernier trajet de retour.}\par\addvspace{0.4em}
\end{document}
