\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}{La tournée du facteur}
\newcommand{\soustitre}{Probl\`eme --- Fiche n\textdegree 265}

\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/facteur_sans_retour.php?x=265}\\[2pt]
    {\small\ttfamily\bfseries\color{red} EULC0265}
\end{minipage}%
}
}

\begin{document}

\begin{center}
    \small Un facteur veut parcourir toutes les rues de son quartier en n'empruntant chacune qu'une seule fois. Selon le plan, c'est tantôt facile, tantôt impossible — et l'on peut le dire d'avance, sans essayer, en regardant simplement combien de rues aboutissent à chaque carrefour.
\end{center}
\vspace{0.5em}
\sloppy
\needspace{5\baselineskip}
\subsection*{\textcolor{red}{La tournée du facteur}}
\noindent Voici le plan d'un quartier.\par\addvspace{0.35em}
\needspace{3\baselineskip}
\begin{center}
\begin{tikzpicture}[scale=0.6878, line join=round, line cap=round]
\draw[line width=0.5pt] (3.653,8.852) -- (3.878,8.802) -- (4.104,8.757) -- (4.331,8.717) -- (4.559,8.683) -- (4.788,8.654) -- (5.018,8.631) -- (5.248,8.613) -- (5.478,8.601) -- (5.709,8.593) -- (5.939,8.592) -- (6.17,8.595) -- (6.4,8.604) -- (6.63,8.619) -- (6.86,8.639);
\draw[line width=0.5pt] (3.653,8.852) -- (3.721,8.651) -- (3.785,8.449) -- (3.844,8.246) -- (3.898,8.041) -- (3.947,7.835) -- (3.992,7.627) -- (4.031,7.419) -- (4.066,7.21) -- (4.096,7.0) -- (4.12,6.789) -- (4.14,6.578) -- (4.155,6.367) -- (4.165,6.155) -- (4.17,5.944);
\draw[line width=0.5pt] (8.783,8.76) -- (8.646,8.772) -- (8.508,8.781) -- (8.37,8.787) -- (8.231,8.79) -- (8.093,8.789) -- (7.955,8.786) -- (7.817,8.779) -- (7.679,8.768) -- (7.541,8.755) -- (7.404,8.738) -- (7.267,8.718) -- (7.131,8.695) -- (6.995,8.669) -- (6.86,8.639);
\draw[line width=0.5pt] (8.783,8.76) -- (8.83,8.603) -- (8.874,8.445) -- (8.913,8.286) -- (8.949,8.127) -- (8.981,7.966) -- (9.009,7.805) -- (9.034,7.643) -- (9.054,7.481) -- (9.071,7.318) -- (9.084,7.155) -- (9.094,6.991) -- (9.099,6.828) -- (9.1,6.664) -- (9.098,6.5);
\draw[line width=0.5pt] (3.729,1.979) -- (3.572,1.954) -- (3.415,1.925) -- (3.258,1.892) -- (3.103,1.856) -- (2.948,1.816) -- (2.794,1.772) -- (2.641,1.725) -- (2.49,1.674) -- (2.339,1.62) -- (2.19,1.562) -- (2.043,1.501) -- (1.896,1.436) -- (1.752,1.368) -- (1.609,1.296);
\draw[line width=0.5pt] (9.19,1.958) -- (9.353,1.971) -- (9.515,1.98) -- (9.678,1.985) -- (9.841,1.987) -- (10.005,1.984) -- (10.168,1.978) -- (10.331,1.968) -- (10.493,1.954) -- (10.655,1.937) -- (10.817,1.915) -- (10.978,1.89) -- (11.139,1.861) -- (11.298,1.828) -- (11.457,1.791);
\draw[line width=0.5pt] (6.86,8.639) -- (6.995,8.463) -- (7.134,8.29) -- (7.278,8.121) -- (7.425,7.955) -- (7.577,7.792) -- (7.732,7.633) -- (7.891,7.477) -- (8.053,7.326) -- (8.219,7.178) -- (8.388,7.034) -- (8.561,6.894) -- (8.737,6.759) -- (8.916,6.627) -- (9.098,6.5);
\draw[line width=0.5pt] (6.86,8.639) -- (6.699,8.419) -- (6.532,8.202) -- (6.361,7.989) -- (6.184,7.781) -- (6.003,7.576) -- (5.817,7.376) -- (5.626,7.18) -- (5.431,6.989) -- (5.231,6.803) -- (5.027,6.621) -- (4.818,6.444) -- (4.606,6.272) -- (4.39,6.105) -- (4.17,5.944);
\draw[line width=0.5pt] (9.098,6.5) -- (8.911,6.492) -- (8.725,6.479) -- (8.539,6.462) -- (8.354,6.44) -- (8.169,6.414) -- (7.985,6.384) -- (7.801,6.349) -- (7.618,6.31) -- (7.437,6.267) -- (7.256,6.219) -- (7.076,6.167) -- (6.898,6.111) -- (6.722,6.051) -- (6.546,5.987) -- (6.378,5.958) -- (6.21,5.933) -- (6.041,5.912) -- (5.871,5.895) -- (5.701,5.882) -- (5.53,5.872) -- (5.36,5.867) -- (5.189,5.866) -- (5.019,5.869) -- (4.848,5.876) -- (4.678,5.887) -- (4.508,5.902) -- (4.338,5.921) -- (4.17,5.944);
\draw[line width=0.5pt] (9.098,6.5) -- (9.303,6.353) -- (9.504,6.201) -- (9.702,6.045) -- (9.896,5.883) -- (10.086,5.718) -- (10.273,5.547) -- (10.455,5.373) -- (10.633,5.194) -- (10.807,5.011) -- (10.977,4.824) -- (11.142,4.633) -- (11.302,4.438) -- (11.458,4.24) -- (11.609,4.038);
\draw[line width=0.5pt] (4.17,5.944) -- (4.341,5.794) -- (4.517,5.649) -- (4.696,5.508) -- (4.878,5.371) -- (5.063,5.238) -- (5.252,5.11) -- (5.443,4.986) -- (5.638,4.867) -- (5.835,4.752) -- (6.034,4.642) -- (6.237,4.536) -- (6.441,4.436) -- (6.648,4.34) -- (6.857,4.25);
\draw[line width=0.5pt] (4.17,5.944) -- (4.029,5.762) -- (3.885,5.583) -- (3.736,5.408) -- (3.583,5.236) -- (3.426,5.067) -- (3.265,4.903) -- (3.1,4.742) -- (2.932,4.585) -- (2.76,4.433) -- (2.584,4.284) -- (2.405,4.14) -- (2.223,3.999) -- (2.037,3.864) -- (1.848,3.732);
\draw[line width=0.5pt] (4.17,5.944) -- (4.179,5.773) -- (4.193,5.603) -- (4.21,5.433) -- (4.232,5.264) -- (4.258,5.095) -- (4.287,4.927) -- (4.321,4.759) -- (4.358,4.592) -- (4.4,4.427) -- (4.445,4.262) -- (4.494,4.098) -- (4.547,3.936) -- (4.604,3.775) -- (4.665,3.615);
\draw[line width=0.5pt] (6.857,4.25) -- (6.66,4.055) -- (6.459,3.864) -- (6.253,3.678) -- (6.043,3.498) -- (5.828,3.322) -- (5.609,3.151) -- (5.387,2.985) -- (5.161,2.825) -- (4.93,2.67) -- (4.697,2.52) -- (4.46,2.377) -- (4.219,2.238) -- (3.976,2.106) -- (3.729,1.979);
\draw[line width=0.5pt] (6.857,4.25) -- (7.004,4.205) -- (7.153,4.164) -- (7.302,4.127) -- (7.452,4.093) -- (7.603,4.062) -- (7.755,4.035) -- (7.908,4.012) -- (8.06,3.992) -- (8.214,3.976) -- (8.367,3.963) -- (8.521,3.954) -- (8.675,3.949) -- (8.829,3.947) -- (8.983,3.949);
\draw[line width=0.5pt] (6.857,4.25) -- (6.709,4.181) -- (6.559,4.115) -- (6.407,4.053) -- (6.254,3.995) -- (6.099,3.94) -- (5.944,3.889) -- (5.787,3.842) -- (5.629,3.798) -- (5.47,3.758) -- (5.31,3.722) -- (5.15,3.69) -- (4.989,3.661) -- (4.827,3.636) -- (4.665,3.615);
\draw[line width=0.5pt] (11.609,4.038) -- (11.574,3.88) -- (11.542,3.722) -- (11.514,3.563) -- (11.49,3.403) -- (11.47,3.243) -- (11.453,3.082) -- (11.441,2.921) -- (11.432,2.759) -- (11.426,2.598) -- (11.425,2.436) -- (11.427,2.275) -- (11.433,2.113) -- (11.443,1.952) -- (11.457,1.791);
\draw[line width=0.5pt] (8.983,3.949) -- (9.019,3.811) -- (9.053,3.671) -- (9.082,3.53) -- (9.109,3.389) -- (9.132,3.247) -- (9.152,3.105) -- (9.169,2.962) -- (9.182,2.819) -- (9.192,2.676) -- (9.198,2.532) -- (9.201,2.389) -- (9.201,2.245) -- (9.197,2.102) -- (9.19,1.958);
\draw[line width=0.5pt] (1.848,3.732) -- (1.962,3.587) -- (2.08,3.445) -- (2.201,3.306) -- (2.325,3.17) -- (2.453,3.036) -- (2.583,2.905) -- (2.717,2.778) -- (2.853,2.654) -- (2.992,2.533) -- (3.135,2.415) -- (3.279,2.301) -- (3.427,2.19) -- (3.577,2.083) -- (3.729,1.979);
\draw[line width=0.5pt] (1.848,3.732) -- (1.858,3.557) -- (1.864,3.382) -- (1.865,3.206) -- (1.862,3.03) -- (1.855,2.855) -- (1.844,2.68) -- (1.829,2.504) -- (1.81,2.33) -- (1.787,2.156) -- (1.759,1.982) -- (1.728,1.809) -- (1.692,1.637) -- (1.653,1.466) -- (1.609,1.296);
\draw[line width=0.5pt] (1.848,3.732) -- (2.047,3.693) -- (2.246,3.659) -- (2.446,3.629) -- (2.647,3.604) -- (2.848,3.584) -- (3.05,3.568) -- (3.252,3.558) -- (3.454,3.552) -- (3.656,3.55) -- (3.858,3.554) -- (4.061,3.562) -- (4.262,3.575) -- (4.464,3.593) -- (4.665,3.615);
\draw[line width=0.5pt] (4.665,3.615) -- (4.616,3.489) -- (4.565,3.364) -- (4.511,3.24) -- (4.453,3.118) -- (4.393,2.997) -- (4.33,2.877) -- (4.265,2.759) -- (4.196,2.642) -- (4.125,2.527) -- (4.051,2.414) -- (3.974,2.302) -- (3.895,2.192) -- (3.814,2.085) -- (3.729,1.979);
\filldraw[fill=red!16, draw=black, line width=0.5pt] (3.813,8.852) -- (3.792,8.932) -- (3.733,8.99) -- (3.653,9.012) -- (3.573,8.99) -- (3.514,8.932) -- (3.493,8.852) -- (3.514,8.772) -- (3.573,8.713) -- (3.653,8.692) -- (3.733,8.713) -- (3.792,8.772) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (8.943,8.76) -- (8.922,8.84) -- (8.863,8.898) -- (8.783,8.92) -- (8.703,8.898) -- (8.645,8.84) -- (8.623,8.76) -- (8.645,8.68) -- (8.703,8.621) -- (8.783,8.6) -- (8.863,8.621) -- (8.922,8.68) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (7.02,8.639) -- (6.998,8.719) -- (6.94,8.778) -- (6.86,8.799) -- (6.78,8.778) -- (6.721,8.719) -- (6.7,8.639) -- (6.721,8.559) -- (6.78,8.5) -- (6.86,8.479) -- (6.94,8.5) -- (6.998,8.559) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (9.258,6.5) -- (9.236,6.58) -- (9.178,6.639) -- (9.098,6.66) -- (9.018,6.639) -- (8.959,6.58) -- (8.938,6.5) -- (8.959,6.42) -- (9.018,6.362) -- (9.098,6.34) -- (9.178,6.362) -- (9.236,6.42) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (4.33,5.944) -- (4.308,6.024) -- (4.25,6.082) -- (4.17,6.104) -- (4.09,6.082) -- (4.031,6.024) -- (4.01,5.944) -- (4.031,5.864) -- (4.09,5.805) -- (4.17,5.784) -- (4.25,5.805) -- (4.308,5.864) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (7.017,4.25) -- (6.996,4.33) -- (6.937,4.388) -- (6.857,4.41) -- (6.777,4.388) -- (6.718,4.33) -- (6.697,4.25) -- (6.718,4.17) -- (6.777,4.111) -- (6.857,4.09) -- (6.937,4.111) -- (6.996,4.17) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (11.769,4.038) -- (11.748,4.118) -- (11.689,4.176) -- (11.609,4.198) -- (11.529,4.176) -- (11.471,4.118) -- (11.449,4.038) -- (11.471,3.958) -- (11.529,3.899) -- (11.609,3.878) -- (11.689,3.899) -- (11.748,3.958) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (9.143,3.949) -- (9.121,4.029) -- (9.063,4.088) -- (8.983,4.109) -- (8.903,4.088) -- (8.844,4.029) -- (8.823,3.949) -- (8.844,3.869) -- (8.903,3.811) -- (8.983,3.789) -- (9.063,3.811) -- (9.121,3.869) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (2.008,3.732) -- (1.987,3.812) -- (1.928,3.871) -- (1.848,3.892) -- (1.768,3.871) -- (1.71,3.812) -- (1.688,3.732) -- (1.71,3.652) -- (1.768,3.594) -- (1.848,3.572) -- (1.928,3.594) -- (1.987,3.652) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (4.825,3.615) -- (4.803,3.695) -- (4.745,3.754) -- (4.665,3.775) -- (4.585,3.754) -- (4.526,3.695) -- (4.505,3.615) -- (4.526,3.535) -- (4.585,3.477) -- (4.665,3.455) -- (4.745,3.477) -- (4.803,3.535) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (3.889,1.979) -- (3.868,2.059) -- (3.809,2.118) -- (3.729,2.139) -- (3.649,2.118) -- (3.591,2.059) -- (3.569,1.979) -- (3.591,1.899) -- (3.649,1.84) -- (3.729,1.819) -- (3.809,1.84) -- (3.868,1.899) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (9.35,1.958) -- (9.329,2.038) -- (9.27,2.097) -- (9.19,2.118) -- (9.11,2.097) -- (9.052,2.038) -- (9.03,1.958) -- (9.052,1.878) -- (9.11,1.82) -- (9.19,1.798) -- (9.27,1.82) -- (9.329,1.878) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (11.617,1.791) -- (11.596,1.871) -- (11.537,1.93) -- (11.457,1.951) -- (11.377,1.93) -- (11.319,1.871) -- (11.297,1.791) -- (11.319,1.711) -- (11.377,1.653) -- (11.457,1.631) -- (11.537,1.653) -- (11.596,1.711) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (1.769,1.296) -- (1.748,1.376) -- (1.689,1.435) -- (1.609,1.456) -- (1.529,1.435) -- (1.471,1.376) -- (1.449,1.296) -- (1.471,1.216) -- (1.529,1.158) -- (1.609,1.136) -- (1.689,1.158) -- (1.748,1.216) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (5.609,8.932) -- (5.563,9.102) -- (5.439,9.227) -- (5.269,9.272) -- (5.099,9.227) -- (4.974,9.102) -- (4.929,8.932) -- (4.974,8.762) -- (5.099,8.638) -- (5.269,8.592) -- (5.439,8.638) -- (5.563,8.762) -- cycle;
\node at (5.269,8.932) {\scalebox{1.454}{\small 1}};
\filldraw[fill=white, draw=black, line width=0.5pt] (4.686,7.475) -- (4.641,7.645) -- (4.516,7.769) -- (4.346,7.815) -- (4.176,7.769) -- (4.052,7.645) -- (4.006,7.475) -- (4.052,7.305) -- (4.176,7.181) -- (4.346,7.135) -- (4.516,7.181) -- (4.641,7.305) -- cycle;
\node at (4.346,7.475) {\scalebox{1.454}{\small 2}};
\filldraw[fill=white, draw=black, line width=0.5pt] (8.177,8.459) -- (8.131,8.629) -- (8.007,8.754) -- (7.837,8.799) -- (7.667,8.754) -- (7.542,8.629) -- (7.497,8.459) -- (7.542,8.289) -- (7.667,8.165) -- (7.837,8.119) -- (8.007,8.165) -- (8.131,8.289) -- cycle;
\node at (7.837,8.459) {\scalebox{1.454}{\small 3}};
\filldraw[fill=white, draw=black, line width=0.5pt] (9.691,7.687) -- (9.645,7.857) -- (9.521,7.982) -- (9.351,8.027) -- (9.181,7.982) -- (9.056,7.857) -- (9.011,7.687) -- (9.056,7.517) -- (9.181,7.393) -- (9.351,7.347) -- (9.521,7.393) -- (9.645,7.517) -- cycle;
\node at (9.351,7.687) {\scalebox{1.454}{\small 4}};
\filldraw[fill=white, draw=black, line width=0.5pt] (3.079,1.421) -- (3.034,1.591) -- (2.909,1.715) -- (2.739,1.761) -- (2.569,1.715) -- (2.445,1.591) -- (2.399,1.421) -- (2.445,1.251) -- (2.569,1.126) -- (2.739,1.081) -- (2.909,1.126) -- (3.034,1.251) -- cycle;
\node at (2.739,1.421) {\scalebox{1.454}{\small 5}};
\filldraw[fill=white, draw=black, line width=0.5pt] (10.694,2.287) -- (10.649,2.457) -- (10.524,2.582) -- (10.354,2.627) -- (10.184,2.582) -- (10.06,2.457) -- (10.014,2.287) -- (10.06,2.117) -- (10.184,1.993) -- (10.354,1.947) -- (10.524,1.993) -- (10.649,2.117) -- cycle;
\node at (10.354,2.287) {\scalebox{1.454}{\small 6}};
\filldraw[fill=white, draw=black, line width=0.5pt] (8.452,7.709) -- (8.406,7.879) -- (8.282,8.003) -- (8.112,8.049) -- (7.942,8.003) -- (7.817,7.879) -- (7.772,7.709) -- (7.817,7.539) -- (7.942,7.414) -- (8.112,7.369) -- (8.282,7.414) -- (8.406,7.539) -- cycle;
\node at (8.112,7.709) {\scalebox{1.454}{\small 7}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.192,6.954) -- (6.147,7.124) -- (6.022,7.249) -- (5.852,7.294) -- (5.682,7.249) -- (5.558,7.124) -- (5.512,6.954) -- (5.558,6.784) -- (5.682,6.66) -- (5.852,6.614) -- (6.022,6.66) -- (6.147,6.784) -- cycle;
\node at (5.852,6.954) {\scalebox{1.454}{\small 8}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.97,5.678) -- (6.925,5.848) -- (6.8,5.973) -- (6.63,6.018) -- (6.46,5.973) -- (6.336,5.848) -- (6.29,5.678) -- (6.336,5.508) -- (6.46,5.384) -- (6.63,5.338) -- (6.8,5.384) -- (6.925,5.508) -- cycle;
\node at (6.63,5.678) {\scalebox{1.454}{\small 9}};
\filldraw[fill=white, draw=black, line width=0.5pt] (11.019,5.601) -- (10.974,5.771) -- (10.849,5.896) -- (10.679,5.941) -- (10.509,5.896) -- (10.385,5.771) -- (10.339,5.601) -- (10.385,5.431) -- (10.509,5.307) -- (10.679,5.261) -- (10.849,5.307) -- (10.974,5.431) -- cycle;
\node at (10.679,5.601) {\scalebox{1.454}{\small 10}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.954,5.257) -- (5.908,5.427) -- (5.784,5.551) -- (5.614,5.597) -- (5.444,5.551) -- (5.32,5.427) -- (5.274,5.257) -- (5.32,5.087) -- (5.444,4.962) -- (5.614,4.917) -- (5.784,4.962) -- (5.908,5.087) -- cycle;
\node at (5.614,5.257) {\scalebox{1.454}{\small 11}};
\filldraw[fill=white, draw=black, line width=0.5pt] (3.661,4.511) -- (3.615,4.681) -- (3.491,4.805) -- (3.321,4.851) -- (3.151,4.805) -- (3.026,4.681) -- (2.981,4.511) -- (3.026,4.341) -- (3.151,4.216) -- (3.321,4.171) -- (3.491,4.216) -- (3.615,4.341) -- cycle;
\node at (3.321,4.511) {\scalebox{1.454}{\small 12}};
\filldraw[fill=white, draw=black, line width=0.5pt] (4.974,4.826) -- (4.928,4.996) -- (4.804,5.12) -- (4.634,5.166) -- (4.464,5.12) -- (4.34,4.996) -- (4.294,4.826) -- (4.34,4.656) -- (4.464,4.531) -- (4.634,4.486) -- (4.804,4.531) -- (4.928,4.656) -- cycle;
\node at (4.634,4.826) {\scalebox{1.454}{\small 13}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.915,2.726) -- (5.869,2.896) -- (5.745,3.021) -- (5.575,3.066) -- (5.405,3.021) -- (5.28,2.896) -- (5.235,2.726) -- (5.28,2.556) -- (5.405,2.432) -- (5.575,2.386) -- (5.745,2.432) -- (5.869,2.556) -- cycle;
\node at (5.575,2.726) {\scalebox{1.454}{\small 14}};
\filldraw[fill=white, draw=black, line width=0.5pt] (8.292,4.329) -- (8.247,4.499) -- (8.122,4.623) -- (7.952,4.669) -- (7.782,4.623) -- (7.658,4.499) -- (7.612,4.329) -- (7.658,4.159) -- (7.782,4.034) -- (7.952,3.989) -- (8.122,4.034) -- (8.247,4.159) -- cycle;
\node at (7.952,4.329) {\scalebox{1.454}{\small 15}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.216,3.535) -- (6.17,3.705) -- (6.046,3.829) -- (5.876,3.875) -- (5.706,3.829) -- (5.581,3.705) -- (5.536,3.535) -- (5.581,3.365) -- (5.706,3.24) -- (5.876,3.195) -- (6.046,3.24) -- (6.17,3.365) -- cycle;
\node at (5.876,3.535) {\scalebox{1.454}{\small 16}};
\filldraw[fill=white, draw=black, line width=0.5pt] (12.1,2.899) -- (12.054,3.069) -- (11.93,3.193) -- (11.76,3.239) -- (11.59,3.193) -- (11.465,3.069) -- (11.42,2.899) -- (11.465,2.729) -- (11.59,2.605) -- (11.76,2.559) -- (11.93,2.605) -- (12.054,2.729) -- cycle;
\node at (11.76,2.899) {\scalebox{1.454}{\small 17}};
\filldraw[fill=white, draw=black, line width=0.5pt] (9.827,2.995) -- (9.781,3.165) -- (9.657,3.29) -- (9.487,3.335) -- (9.317,3.29) -- (9.192,3.165) -- (9.147,2.995) -- (9.192,2.825) -- (9.317,2.701) -- (9.487,2.655) -- (9.657,2.701) -- (9.781,2.825) -- cycle;
\node at (9.487,2.995) {\scalebox{1.454}{\small 18}};
\filldraw[fill=white, draw=black, line width=0.5pt] (3.275,3.012) -- (3.229,3.182) -- (3.105,3.307) -- (2.935,3.352) -- (2.765,3.307) -- (2.64,3.182) -- (2.595,3.012) -- (2.64,2.842) -- (2.765,2.718) -- (2.935,2.672) -- (3.105,2.718) -- (3.229,2.842) -- cycle;
\node at (2.935,3.012) {\scalebox{1.454}{\small 19}};
\filldraw[fill=white, draw=black, line width=0.5pt] (2.488,2.473) -- (2.442,2.643) -- (2.318,2.768) -- (2.148,2.813) -- (1.978,2.768) -- (1.853,2.643) -- (1.808,2.473) -- (1.853,2.303) -- (1.978,2.179) -- (2.148,2.133) -- (2.318,2.179) -- (2.442,2.303) -- cycle;
\node at (2.148,2.473) {\scalebox{1.454}{\small 20}};
\filldraw[fill=white, draw=black, line width=0.5pt] (3.216,3.903) -- (3.171,4.073) -- (3.046,4.197) -- (2.876,4.243) -- (2.706,4.197) -- (2.582,4.073) -- (2.536,3.903) -- (2.582,3.733) -- (2.706,3.608) -- (2.876,3.563) -- (3.046,3.608) -- (3.171,3.733) -- cycle;
\node at (2.876,3.903) {\scalebox{1.454}{\small 21}};
\filldraw[fill=white, draw=black, line width=0.5pt] (4.882,2.6) -- (4.837,2.77) -- (4.712,2.894) -- (4.542,2.94) -- (4.372,2.894) -- (4.248,2.77) -- (4.202,2.6) -- (4.248,2.43) -- (4.372,2.305) -- (4.542,2.26) -- (4.712,2.305) -- (4.837,2.43) -- cycle;
\node at (4.542,2.6) {\scalebox{1.454}{\small 22}};
\filldraw[fill=yellow!35, draw=black, line width=0.5pt] (8.798,6.2) -- (9.398,6.2) -- (9.398,6.8) -- (8.798,6.8) -- cycle;
\node at (9.098,6.5) {\scalebox{1.454}{\small a}};
\filldraw[fill=black!14, draw=black, line width=0.5pt] (4.559,4.573) -- (5.159,4.573) -- (5.159,5.173) -- (4.559,5.173) -- cycle;
\node at (4.859,4.873) {\scalebox{1.454}{\small b}};
\filldraw[fill=green!18, draw=black, line width=0.5pt] (4.982,1.227) -- (5.582,1.227) -- (5.582,1.827) -- (4.982,1.827) -- cycle;
\node at (5.282,1.527) {\scalebox{1.454}{\small c}};
\filldraw[fill=black!14, draw=black, line width=0.5pt] (4.62,5.888) -- (5.22,5.888) -- (5.22,6.488) -- (4.62,6.488) -- cycle;
\node at (4.92,6.188) {\scalebox{1.454}{\small d}};
\node at (3.295,9.358) {\scalebox{1.454}{\small S0}};
\node at (9.074,9.307) {\scalebox{1.454}{\small S1}};
\node at (6.899,9.258) {\scalebox{1.454}{\small S2}};
\node at (9.597,6.868) {\scalebox{1.454}{\small S3}};
\node at (3.621,6.232) {\scalebox{1.454}{\small S4}};
\node at (7.176,3.718) {\scalebox{1.454}{\small S5}};
\node at (12.224,3.961) {\scalebox{1.454}{\small S6}};
\node at (9.577,3.771) {\scalebox{1.454}{\small S7}};
\node at (1.24,3.613) {\scalebox{1.454}{\small S8}};
\node at (4.119,3.321) {\scalebox{1.454}{\small S9}};
\node at (3.276,1.556) {\scalebox{1.454}{\small S10}};
\node at (9.618,1.51) {\scalebox{1.454}{\small S11}};
\node at (11.991,1.475) {\scalebox{1.454}{\small S12}};
\node at (1.095,0.95) {\scalebox{1.454}{\small S13}};
\draw[line width=0.5pt] (12.909,7.902) -- (12.909,9.002);
\draw[line width=0.5pt] (12.678,8.617) -- (12.909,9.002) -- (13.14,8.617);
\draw[line width=0.5pt] (12.607,8.452) -- (13.212,8.452);
\node at (12.909,9.387) {\scalebox{1.454}{\small N}};
\end{tikzpicture}
\end{center}
\noindent \textbf{Le facteur part de la poste et doit emprunter chaque rue exactement une fois. Il n'est pas obligé d'y revenir : il termine sa tournée où il veut.}\par\addvspace{0.35em}
\begin{center}
\renewcommand{\arraystretch}{1.35}
\begin{tabular}{|c|c|c|c|}
\hline
\cellcolor{blue!7}\bfseries Les rues & \cellcolor{blue!7}\bfseries  & \cellcolor{blue!7}\bfseries Les carrefours & \cellcolor{blue!7}\bfseries Les bâtiments \\ \hline
① allée des Peupliers & ⑫ rue Pasteur & S0 Place de l'Église & \textbf{a} la poste \\ \hline
② chemin du Lavoir & ⑬ boulevard du Parc & S1 Place Sainte-Croix & \textbf{b} le cimetière \\ \hline
③ rue de la Mairie & ⑭ passage du Marché & S2 Rond-point du Stade & \textbf{c} la salle des fêtes \\ \hline
④ rue des Écoles & ⑮ rue de la Poste & S3 Rond-point du Pont & \textbf{d} le stade \\ \hline
⑤ chemin Creux & ⑯ chemin de Ronde & S4 Carrefour du Moulin &  \\ \hline
⑥ rue du Moulin & ⑰ rue Haute & S5 Carrefour du Lavoir &  \\ \hline
⑦ rue du Stade & ⑱ rue du Pont & S6 Place des Tanneurs &  \\ \hline
⑧ quai aux Fleurs & ⑲ rue Verte & S7 Coin du Lavoir &  \\ \hline
⑨ rue des Jardins & ⑳ rue Neuve & S8 Rond-point des Vaches &  \\ \hline
⑩ rue des Lilas & 21 avenue de la Gare & S9 Carrefour Saint-Roch &  \\ \hline
⑪ venelle du Chat & 22 rue du Four & S10 Rond-point de la Poste &  \\ \hline
 &  & S11 Place de la Fontaine &  \\ \hline
 &  & S12 Placette des Ormes &  \\ \hline
 &  & S13 Fontaine Notre-Dame &  \\ \hline
\end{tabular}
\end{center}
\noindent{\small\itshape Légende du plan}\par\addvspace{0.4em}
\noindent Les questions se suivent : la première n'est qu'un comptage, la dernière demande une preuve.\par\addvspace{0.45em}
\begin{enumerate}
  \item Pour \textbf{chaque carrefour}, compter le nombre de rues qui y aboutissent. Présenter les résultats dans un tableau.
  \item Le facteur imagine sa tournée. À chaque fois qu'il \textbf{traverse} un carrefour, combien de rues utilise-t-il ? Qu'en déduire pour les carrefours où aboutit un nombre \textbf{impair} de rues ?
  \item \textbf{Le facteur peut-il faire sa tournée en partant de la poste ?} Si oui, décrire un trajet possible ; sinon, démontrer que c'est impossible.
  \item Si ce n'est pas possible : une tournée existe-t-elle \textbf{malgré tout} dans ce quartier, en partant d'ailleurs ? Si oui, où faudrait-il installer la poste — et le facteur y reviendrait-il ?
\end{enumerate}
\newpage
\section*{\textcolor{red}{Correction}}
\needspace{5\baselineskip}
\subsection*{\textcolor{red}{La tournée du facteur — Correction}}
\needspace{3\baselineskip}
\begin{center}
\begin{tikzpicture}[scale=0.6154, line join=round, line cap=round]
\draw[line width=0.5pt] (3.653,8.852) -- (3.878,8.802) -- (4.104,8.757) -- (4.331,8.717) -- (4.559,8.683) -- (4.788,8.654) -- (5.018,8.631) -- (5.248,8.613) -- (5.478,8.601) -- (5.709,8.593) -- (5.939,8.592) -- (6.17,8.595) -- (6.4,8.604) -- (6.63,8.619) -- (6.86,8.639);
\draw[line width=0.5pt] (3.653,8.852) -- (3.721,8.651) -- (3.785,8.449) -- (3.844,8.246) -- (3.898,8.041) -- (3.947,7.835) -- (3.992,7.627) -- (4.031,7.419) -- (4.066,7.21) -- (4.096,7.0) -- (4.12,6.789) -- (4.14,6.578) -- (4.155,6.367) -- (4.165,6.155) -- (4.17,5.944);
\draw[line width=0.5pt] (8.783,8.76) -- (8.646,8.772) -- (8.508,8.781) -- (8.37,8.787) -- (8.231,8.79) -- (8.093,8.789) -- (7.955,8.786) -- (7.817,8.779) -- (7.679,8.768) -- (7.541,8.755) -- (7.404,8.738) -- (7.267,8.718) -- (7.131,8.695) -- (6.995,8.669) -- (6.86,8.639);
\draw[line width=0.5pt] (8.783,8.76) -- (8.83,8.603) -- (8.874,8.445) -- (8.913,8.286) -- (8.949,8.127) -- (8.981,7.966) -- (9.009,7.805) -- (9.034,7.643) -- (9.054,7.481) -- (9.071,7.318) -- (9.084,7.155) -- (9.094,6.991) -- (9.099,6.828) -- (9.1,6.664) -- (9.098,6.5);
\draw[line width=0.5pt] (3.729,1.979) -- (3.572,1.954) -- (3.415,1.925) -- (3.258,1.892) -- (3.103,1.856) -- (2.948,1.816) -- (2.794,1.772) -- (2.641,1.725) -- (2.49,1.674) -- (2.339,1.62) -- (2.19,1.562) -- (2.043,1.501) -- (1.896,1.436) -- (1.752,1.368) -- (1.609,1.296);
\draw[line width=0.5pt] (9.19,1.958) -- (9.353,1.971) -- (9.515,1.98) -- (9.678,1.985) -- (9.841,1.987) -- (10.005,1.984) -- (10.168,1.978) -- (10.331,1.968) -- (10.493,1.954) -- (10.655,1.937) -- (10.817,1.915) -- (10.978,1.89) -- (11.139,1.861) -- (11.298,1.828) -- (11.457,1.791);
\draw[line width=0.5pt] (6.86,8.639) -- (6.995,8.463) -- (7.134,8.29) -- (7.278,8.121) -- (7.425,7.955) -- (7.577,7.792) -- (7.732,7.633) -- (7.891,7.477) -- (8.053,7.326) -- (8.219,7.178) -- (8.388,7.034) -- (8.561,6.894) -- (8.737,6.759) -- (8.916,6.627) -- (9.098,6.5);
\draw[line width=0.5pt] (6.86,8.639) -- (6.699,8.419) -- (6.532,8.202) -- (6.361,7.989) -- (6.184,7.781) -- (6.003,7.576) -- (5.817,7.376) -- (5.626,7.18) -- (5.431,6.989) -- (5.231,6.803) -- (5.027,6.621) -- (4.818,6.444) -- (4.606,6.272) -- (4.39,6.105) -- (4.17,5.944);
\draw[line width=0.5pt] (9.098,6.5) -- (8.911,6.492) -- (8.725,6.479) -- (8.539,6.462) -- (8.354,6.44) -- (8.169,6.414) -- (7.985,6.384) -- (7.801,6.349) -- (7.618,6.31) -- (7.437,6.267) -- (7.256,6.219) -- (7.076,6.167) -- (6.898,6.111) -- (6.722,6.051) -- (6.546,5.987) -- (6.378,5.958) -- (6.21,5.933) -- (6.041,5.912) -- (5.871,5.895) -- (5.701,5.882) -- (5.53,5.872) -- (5.36,5.867) -- (5.189,5.866) -- (5.019,5.869) -- (4.848,5.876) -- (4.678,5.887) -- (4.508,5.902) -- (4.338,5.921) -- (4.17,5.944);
\draw[line width=0.5pt] (9.098,6.5) -- (9.303,6.353) -- (9.504,6.201) -- (9.702,6.045) -- (9.896,5.883) -- (10.086,5.718) -- (10.273,5.547) -- (10.455,5.373) -- (10.633,5.194) -- (10.807,5.011) -- (10.977,4.824) -- (11.142,4.633) -- (11.302,4.438) -- (11.458,4.24) -- (11.609,4.038);
\draw[line width=0.5pt] (4.17,5.944) -- (4.341,5.794) -- (4.517,5.649) -- (4.696,5.508) -- (4.878,5.371) -- (5.063,5.238) -- (5.252,5.11) -- (5.443,4.986) -- (5.638,4.867) -- (5.835,4.752) -- (6.034,4.642) -- (6.237,4.536) -- (6.441,4.436) -- (6.648,4.34) -- (6.857,4.25);
\draw[line width=0.5pt] (4.17,5.944) -- (4.029,5.762) -- (3.885,5.583) -- (3.736,5.408) -- (3.583,5.236) -- (3.426,5.067) -- (3.265,4.903) -- (3.1,4.742) -- (2.932,4.585) -- (2.76,4.433) -- (2.584,4.284) -- (2.405,4.14) -- (2.223,3.999) -- (2.037,3.864) -- (1.848,3.732);
\draw[line width=0.5pt] (4.17,5.944) -- (4.179,5.773) -- (4.193,5.603) -- (4.21,5.433) -- (4.232,5.264) -- (4.258,5.095) -- (4.287,4.927) -- (4.321,4.759) -- (4.358,4.592) -- (4.4,4.427) -- (4.445,4.262) -- (4.494,4.098) -- (4.547,3.936) -- (4.604,3.775) -- (4.665,3.615);
\draw[line width=0.5pt] (6.857,4.25) -- (6.66,4.055) -- (6.459,3.864) -- (6.253,3.678) -- (6.043,3.498) -- (5.828,3.322) -- (5.609,3.151) -- (5.387,2.985) -- (5.161,2.825) -- (4.93,2.67) -- (4.697,2.52) -- (4.46,2.377) -- (4.219,2.238) -- (3.976,2.106) -- (3.729,1.979);
\draw[line width=0.5pt] (6.857,4.25) -- (7.004,4.205) -- (7.153,4.164) -- (7.302,4.127) -- (7.452,4.093) -- (7.603,4.062) -- (7.755,4.035) -- (7.908,4.012) -- (8.06,3.992) -- (8.214,3.976) -- (8.367,3.963) -- (8.521,3.954) -- (8.675,3.949) -- (8.829,3.947) -- (8.983,3.949);
\draw[line width=0.5pt] (6.857,4.25) -- (6.709,4.181) -- (6.559,4.115) -- (6.407,4.053) -- (6.254,3.995) -- (6.099,3.94) -- (5.944,3.889) -- (5.787,3.842) -- (5.629,3.798) -- (5.47,3.758) -- (5.31,3.722) -- (5.15,3.69) -- (4.989,3.661) -- (4.827,3.636) -- (4.665,3.615);
\draw[line width=0.5pt] (11.609,4.038) -- (11.574,3.88) -- (11.542,3.722) -- (11.514,3.563) -- (11.49,3.403) -- (11.47,3.243) -- (11.453,3.082) -- (11.441,2.921) -- (11.432,2.759) -- (11.426,2.598) -- (11.425,2.436) -- (11.427,2.275) -- (11.433,2.113) -- (11.443,1.952) -- (11.457,1.791);
\draw[line width=0.5pt] (8.983,3.949) -- (9.019,3.811) -- (9.053,3.671) -- (9.082,3.53) -- (9.109,3.389) -- (9.132,3.247) -- (9.152,3.105) -- (9.169,2.962) -- (9.182,2.819) -- (9.192,2.676) -- (9.198,2.532) -- (9.201,2.389) -- (9.201,2.245) -- (9.197,2.102) -- (9.19,1.958);
\draw[line width=0.5pt] (1.848,3.732) -- (1.962,3.587) -- (2.08,3.445) -- (2.201,3.306) -- (2.325,3.17) -- (2.453,3.036) -- (2.583,2.905) -- (2.717,2.778) -- (2.853,2.654) -- (2.992,2.533) -- (3.135,2.415) -- (3.279,2.301) -- (3.427,2.19) -- (3.577,2.083) -- (3.729,1.979);
\draw[line width=0.5pt] (1.848,3.732) -- (1.858,3.557) -- (1.864,3.382) -- (1.865,3.206) -- (1.862,3.03) -- (1.855,2.855) -- (1.844,2.68) -- (1.829,2.504) -- (1.81,2.33) -- (1.787,2.156) -- (1.759,1.982) -- (1.728,1.809) -- (1.692,1.637) -- (1.653,1.466) -- (1.609,1.296);
\draw[line width=0.5pt] (1.848,3.732) -- (2.047,3.693) -- (2.246,3.659) -- (2.446,3.629) -- (2.647,3.604) -- (2.848,3.584) -- (3.05,3.568) -- (3.252,3.558) -- (3.454,3.552) -- (3.656,3.55) -- (3.858,3.554) -- (4.061,3.562) -- (4.262,3.575) -- (4.464,3.593) -- (4.665,3.615);
\draw[line width=0.5pt] (4.665,3.615) -- (4.616,3.489) -- (4.565,3.364) -- (4.511,3.24) -- (4.453,3.118) -- (4.393,2.997) -- (4.33,2.877) -- (4.265,2.759) -- (4.196,2.642) -- (4.125,2.527) -- (4.051,2.414) -- (3.974,2.302) -- (3.895,2.192) -- (3.814,2.085) -- (3.729,1.979);
\filldraw[fill=red!16, draw=black, line width=0.5pt] (3.813,8.852) -- (3.792,8.932) -- (3.733,8.99) -- (3.653,9.012) -- (3.573,8.99) -- (3.514,8.932) -- (3.493,8.852) -- (3.514,8.772) -- (3.573,8.713) -- (3.653,8.692) -- (3.733,8.713) -- (3.792,8.772) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (8.943,8.76) -- (8.922,8.84) -- (8.863,8.898) -- (8.783,8.92) -- (8.703,8.898) -- (8.645,8.84) -- (8.623,8.76) -- (8.645,8.68) -- (8.703,8.621) -- (8.783,8.6) -- (8.863,8.621) -- (8.922,8.68) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (7.02,8.639) -- (6.998,8.719) -- (6.94,8.778) -- (6.86,8.799) -- (6.78,8.778) -- (6.721,8.719) -- (6.7,8.639) -- (6.721,8.559) -- (6.78,8.5) -- (6.86,8.479) -- (6.94,8.5) -- (6.998,8.559) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (9.258,6.5) -- (9.236,6.58) -- (9.178,6.639) -- (9.098,6.66) -- (9.018,6.639) -- (8.959,6.58) -- (8.938,6.5) -- (8.959,6.42) -- (9.018,6.362) -- (9.098,6.34) -- (9.178,6.362) -- (9.236,6.42) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (4.33,5.944) -- (4.308,6.024) -- (4.25,6.082) -- (4.17,6.104) -- (4.09,6.082) -- (4.031,6.024) -- (4.01,5.944) -- (4.031,5.864) -- (4.09,5.805) -- (4.17,5.784) -- (4.25,5.805) -- (4.308,5.864) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (7.017,4.25) -- (6.996,4.33) -- (6.937,4.388) -- (6.857,4.41) -- (6.777,4.388) -- (6.718,4.33) -- (6.697,4.25) -- (6.718,4.17) -- (6.777,4.111) -- (6.857,4.09) -- (6.937,4.111) -- (6.996,4.17) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (11.769,4.038) -- (11.748,4.118) -- (11.689,4.176) -- (11.609,4.198) -- (11.529,4.176) -- (11.471,4.118) -- (11.449,4.038) -- (11.471,3.958) -- (11.529,3.899) -- (11.609,3.878) -- (11.689,3.899) -- (11.748,3.958) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (9.143,3.949) -- (9.121,4.029) -- (9.063,4.088) -- (8.983,4.109) -- (8.903,4.088) -- (8.844,4.029) -- (8.823,3.949) -- (8.844,3.869) -- (8.903,3.811) -- (8.983,3.789) -- (9.063,3.811) -- (9.121,3.869) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (2.008,3.732) -- (1.987,3.812) -- (1.928,3.871) -- (1.848,3.892) -- (1.768,3.871) -- (1.71,3.812) -- (1.688,3.732) -- (1.71,3.652) -- (1.768,3.594) -- (1.848,3.572) -- (1.928,3.594) -- (1.987,3.652) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (4.825,3.615) -- (4.803,3.695) -- (4.745,3.754) -- (4.665,3.775) -- (4.585,3.754) -- (4.526,3.695) -- (4.505,3.615) -- (4.526,3.535) -- (4.585,3.477) -- (4.665,3.455) -- (4.745,3.477) -- (4.803,3.535) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (3.889,1.979) -- (3.868,2.059) -- (3.809,2.118) -- (3.729,2.139) -- (3.649,2.118) -- (3.591,2.059) -- (3.569,1.979) -- (3.591,1.899) -- (3.649,1.84) -- (3.729,1.819) -- (3.809,1.84) -- (3.868,1.899) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (9.35,1.958) -- (9.329,2.038) -- (9.27,2.097) -- (9.19,2.118) -- (9.11,2.097) -- (9.052,2.038) -- (9.03,1.958) -- (9.052,1.878) -- (9.11,1.82) -- (9.19,1.798) -- (9.27,1.82) -- (9.329,1.878) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (11.617,1.791) -- (11.596,1.871) -- (11.537,1.93) -- (11.457,1.951) -- (11.377,1.93) -- (11.319,1.871) -- (11.297,1.791) -- (11.319,1.711) -- (11.377,1.653) -- (11.457,1.631) -- (11.537,1.653) -- (11.596,1.711) -- cycle;
\filldraw[fill=red!16, draw=black, line width=0.5pt] (1.769,1.296) -- (1.748,1.376) -- (1.689,1.435) -- (1.609,1.456) -- (1.529,1.435) -- (1.471,1.376) -- (1.449,1.296) -- (1.471,1.216) -- (1.529,1.158) -- (1.609,1.136) -- (1.689,1.158) -- (1.748,1.216) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (5.609,8.932) -- (5.563,9.102) -- (5.439,9.227) -- (5.269,9.272) -- (5.099,9.227) -- (4.974,9.102) -- (4.929,8.932) -- (4.974,8.762) -- (5.099,8.638) -- (5.269,8.592) -- (5.439,8.638) -- (5.563,8.762) -- cycle;
\node at (5.269,8.932) {\scalebox{1.625}{\small 1}};
\filldraw[fill=white, draw=black, line width=0.5pt] (4.686,7.475) -- (4.641,7.645) -- (4.516,7.769) -- (4.346,7.815) -- (4.176,7.769) -- (4.052,7.645) -- (4.006,7.475) -- (4.052,7.305) -- (4.176,7.181) -- (4.346,7.135) -- (4.516,7.181) -- (4.641,7.305) -- cycle;
\node at (4.346,7.475) {\scalebox{1.625}{\small 2}};
\filldraw[fill=white, draw=black, line width=0.5pt] (8.177,8.459) -- (8.131,8.629) -- (8.007,8.754) -- (7.837,8.799) -- (7.667,8.754) -- (7.542,8.629) -- (7.497,8.459) -- (7.542,8.289) -- (7.667,8.165) -- (7.837,8.119) -- (8.007,8.165) -- (8.131,8.289) -- cycle;
\node at (7.837,8.459) {\scalebox{1.625}{\small 3}};
\filldraw[fill=white, draw=black, line width=0.5pt] (9.691,7.687) -- (9.645,7.857) -- (9.521,7.982) -- (9.351,8.027) -- (9.181,7.982) -- (9.056,7.857) -- (9.011,7.687) -- (9.056,7.517) -- (9.181,7.393) -- (9.351,7.347) -- (9.521,7.393) -- (9.645,7.517) -- cycle;
\node at (9.351,7.687) {\scalebox{1.625}{\small 4}};
\filldraw[fill=white, draw=black, line width=0.5pt] (3.079,1.421) -- (3.034,1.591) -- (2.909,1.715) -- (2.739,1.761) -- (2.569,1.715) -- (2.445,1.591) -- (2.399,1.421) -- (2.445,1.251) -- (2.569,1.126) -- (2.739,1.081) -- (2.909,1.126) -- (3.034,1.251) -- cycle;
\node at (2.739,1.421) {\scalebox{1.625}{\small 5}};
\filldraw[fill=white, draw=black, line width=0.5pt] (10.694,2.287) -- (10.649,2.457) -- (10.524,2.582) -- (10.354,2.627) -- (10.184,2.582) -- (10.06,2.457) -- (10.014,2.287) -- (10.06,2.117) -- (10.184,1.993) -- (10.354,1.947) -- (10.524,1.993) -- (10.649,2.117) -- cycle;
\node at (10.354,2.287) {\scalebox{1.625}{\small 6}};
\filldraw[fill=white, draw=black, line width=0.5pt] (8.452,7.709) -- (8.406,7.879) -- (8.282,8.003) -- (8.112,8.049) -- (7.942,8.003) -- (7.817,7.879) -- (7.772,7.709) -- (7.817,7.539) -- (7.942,7.414) -- (8.112,7.369) -- (8.282,7.414) -- (8.406,7.539) -- cycle;
\node at (8.112,7.709) {\scalebox{1.625}{\small 7}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.192,6.954) -- (6.147,7.124) -- (6.022,7.249) -- (5.852,7.294) -- (5.682,7.249) -- (5.558,7.124) -- (5.512,6.954) -- (5.558,6.784) -- (5.682,6.66) -- (5.852,6.614) -- (6.022,6.66) -- (6.147,6.784) -- cycle;
\node at (5.852,6.954) {\scalebox{1.625}{\small 8}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.97,5.678) -- (6.925,5.848) -- (6.8,5.973) -- (6.63,6.018) -- (6.46,5.973) -- (6.336,5.848) -- (6.29,5.678) -- (6.336,5.508) -- (6.46,5.384) -- (6.63,5.338) -- (6.8,5.384) -- (6.925,5.508) -- cycle;
\node at (6.63,5.678) {\scalebox{1.625}{\small 9}};
\filldraw[fill=white, draw=black, line width=0.5pt] (11.019,5.601) -- (10.974,5.771) -- (10.849,5.896) -- (10.679,5.941) -- (10.509,5.896) -- (10.385,5.771) -- (10.339,5.601) -- (10.385,5.431) -- (10.509,5.307) -- (10.679,5.261) -- (10.849,5.307) -- (10.974,5.431) -- cycle;
\node at (10.679,5.601) {\scalebox{1.625}{\small 10}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.954,5.257) -- (5.908,5.427) -- (5.784,5.551) -- (5.614,5.597) -- (5.444,5.551) -- (5.32,5.427) -- (5.274,5.257) -- (5.32,5.087) -- (5.444,4.962) -- (5.614,4.917) -- (5.784,4.962) -- (5.908,5.087) -- cycle;
\node at (5.614,5.257) {\scalebox{1.625}{\small 11}};
\filldraw[fill=white, draw=black, line width=0.5pt] (3.661,4.511) -- (3.615,4.681) -- (3.491,4.805) -- (3.321,4.851) -- (3.151,4.805) -- (3.026,4.681) -- (2.981,4.511) -- (3.026,4.341) -- (3.151,4.216) -- (3.321,4.171) -- (3.491,4.216) -- (3.615,4.341) -- cycle;
\node at (3.321,4.511) {\scalebox{1.625}{\small 12}};
\filldraw[fill=white, draw=black, line width=0.5pt] (4.974,4.826) -- (4.928,4.996) -- (4.804,5.12) -- (4.634,5.166) -- (4.464,5.12) -- (4.34,4.996) -- (4.294,4.826) -- (4.34,4.656) -- (4.464,4.531) -- (4.634,4.486) -- (4.804,4.531) -- (4.928,4.656) -- cycle;
\node at (4.634,4.826) {\scalebox{1.625}{\small 13}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.915,2.726) -- (5.869,2.896) -- (5.745,3.021) -- (5.575,3.066) -- (5.405,3.021) -- (5.28,2.896) -- (5.235,2.726) -- (5.28,2.556) -- (5.405,2.432) -- (5.575,2.386) -- (5.745,2.432) -- (5.869,2.556) -- cycle;
\node at (5.575,2.726) {\scalebox{1.625}{\small 14}};
\filldraw[fill=white, draw=black, line width=0.5pt] (8.292,4.329) -- (8.247,4.499) -- (8.122,4.623) -- (7.952,4.669) -- (7.782,4.623) -- (7.658,4.499) -- (7.612,4.329) -- (7.658,4.159) -- (7.782,4.034) -- (7.952,3.989) -- (8.122,4.034) -- (8.247,4.159) -- cycle;
\node at (7.952,4.329) {\scalebox{1.625}{\small 15}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.216,3.535) -- (6.17,3.705) -- (6.046,3.829) -- (5.876,3.875) -- (5.706,3.829) -- (5.581,3.705) -- (5.536,3.535) -- (5.581,3.365) -- (5.706,3.24) -- (5.876,3.195) -- (6.046,3.24) -- (6.17,3.365) -- cycle;
\node at (5.876,3.535) {\scalebox{1.625}{\small 16}};
\filldraw[fill=white, draw=black, line width=0.5pt] (12.1,2.899) -- (12.054,3.069) -- (11.93,3.193) -- (11.76,3.239) -- (11.59,3.193) -- (11.465,3.069) -- (11.42,2.899) -- (11.465,2.729) -- (11.59,2.605) -- (11.76,2.559) -- (11.93,2.605) -- (12.054,2.729) -- cycle;
\node at (11.76,2.899) {\scalebox{1.625}{\small 17}};
\filldraw[fill=white, draw=black, line width=0.5pt] (9.827,2.995) -- (9.781,3.165) -- (9.657,3.29) -- (9.487,3.335) -- (9.317,3.29) -- (9.192,3.165) -- (9.147,2.995) -- (9.192,2.825) -- (9.317,2.701) -- (9.487,2.655) -- (9.657,2.701) -- (9.781,2.825) -- cycle;
\node at (9.487,2.995) {\scalebox{1.625}{\small 18}};
\filldraw[fill=white, draw=black, line width=0.5pt] (3.275,3.012) -- (3.229,3.182) -- (3.105,3.307) -- (2.935,3.352) -- (2.765,3.307) -- (2.64,3.182) -- (2.595,3.012) -- (2.64,2.842) -- (2.765,2.718) -- (2.935,2.672) -- (3.105,2.718) -- (3.229,2.842) -- cycle;
\node at (2.935,3.012) {\scalebox{1.625}{\small 19}};
\filldraw[fill=white, draw=black, line width=0.5pt] (2.488,2.473) -- (2.442,2.643) -- (2.318,2.768) -- (2.148,2.813) -- (1.978,2.768) -- (1.853,2.643) -- (1.808,2.473) -- (1.853,2.303) -- (1.978,2.179) -- (2.148,2.133) -- (2.318,2.179) -- (2.442,2.303) -- cycle;
\node at (2.148,2.473) {\scalebox{1.625}{\small 20}};
\filldraw[fill=white, draw=black, line width=0.5pt] (3.216,3.903) -- (3.171,4.073) -- (3.046,4.197) -- (2.876,4.243) -- (2.706,4.197) -- (2.582,4.073) -- (2.536,3.903) -- (2.582,3.733) -- (2.706,3.608) -- (2.876,3.563) -- (3.046,3.608) -- (3.171,3.733) -- cycle;
\node at (2.876,3.903) {\scalebox{1.625}{\small 21}};
\filldraw[fill=white, draw=black, line width=0.5pt] (4.882,2.6) -- (4.837,2.77) -- (4.712,2.894) -- (4.542,2.94) -- (4.372,2.894) -- (4.248,2.77) -- (4.202,2.6) -- (4.248,2.43) -- (4.372,2.305) -- (4.542,2.26) -- (4.712,2.305) -- (4.837,2.43) -- cycle;
\node at (4.542,2.6) {\scalebox{1.625}{\small 22}};
\filldraw[fill=yellow!35, draw=black, line width=0.5pt] (8.798,6.2) -- (9.398,6.2) -- (9.398,6.8) -- (8.798,6.8) -- cycle;
\node at (9.098,6.5) {\scalebox{1.625}{\small a}};
\filldraw[fill=black!14, draw=black, line width=0.5pt] (4.559,4.573) -- (5.159,4.573) -- (5.159,5.173) -- (4.559,5.173) -- cycle;
\node at (4.859,4.873) {\scalebox{1.625}{\small b}};
\filldraw[fill=green!18, draw=black, line width=0.5pt] (4.982,1.227) -- (5.582,1.227) -- (5.582,1.827) -- (4.982,1.827) -- cycle;
\node at (5.282,1.527) {\scalebox{1.625}{\small c}};
\filldraw[fill=black!14, draw=black, line width=0.5pt] (4.62,5.888) -- (5.22,5.888) -- (5.22,6.488) -- (4.62,6.488) -- cycle;
\node at (4.92,6.188) {\scalebox{1.625}{\small d}};
\node at (3.295,9.358) {\scalebox{1.625}{\small S0}};
\node at (9.074,9.307) {\scalebox{1.625}{\small S1}};
\node at (6.899,9.258) {\scalebox{1.625}{\small S2}};
\node at (9.597,6.868) {\scalebox{1.625}{\small S3}};
\node at (3.621,6.232) {\scalebox{1.625}{\small S4}};
\node at (7.176,3.718) {\scalebox{1.625}{\small S5}};
\node at (12.224,3.961) {\scalebox{1.625}{\small S6}};
\node at (9.577,3.771) {\scalebox{1.625}{\small S7}};
\node at (1.24,3.613) {\scalebox{1.625}{\small S8}};
\node at (4.119,3.321) {\scalebox{1.625}{\small S9}};
\node at (3.276,1.556) {\scalebox{1.625}{\small S10}};
\node at (9.618,1.51) {\scalebox{1.625}{\small S11}};
\node at (11.991,1.475) {\scalebox{1.625}{\small S12}};
\node at (1.095,0.95) {\scalebox{1.625}{\small S13}};
\draw[line width=0.5pt] (12.909,7.902) -- (12.909,9.002);
\draw[line width=0.5pt] (12.678,8.617) -- (12.909,9.002) -- (13.14,8.617);
\draw[line width=0.5pt] (12.607,8.452) -- (13.212,8.452);
\node at (12.909,9.387) {\scalebox{1.625}{\small N}};
\end{tikzpicture}
\end{center}
\noindent \textbf{1.} On compte les rues aboutissant à chaque carrefour :\par\addvspace{0.35em}
\begin{center}
\renewcommand{\arraystretch}{1.35}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
\cellcolor{blue!7}\bfseries Carrefour & \cellcolor{blue!7}\bfseries S0 & \cellcolor{blue!7}\bfseries S1 & \cellcolor{blue!7}\bfseries S2 & \cellcolor{blue!7}\bfseries S3 & \cellcolor{blue!7}\bfseries S4 & \cellcolor{blue!7}\bfseries S5 & \cellcolor{blue!7}\bfseries S6 & \cellcolor{blue!7}\bfseries S7 & \cellcolor{blue!7}\bfseries S8 & \cellcolor{blue!7}\bfseries S9 & \cellcolor{blue!7}\bfseries S10 & \cellcolor{blue!7}\bfseries S11 & \cellcolor{blue!7}\bfseries S12 & \cellcolor{blue!7}\bfseries S13 \\ \hline
Nombre de rues & 2 & 2 & 4 & 4 & 6 & 4 & 2 & 2 & 4 & 4 & 4 & 2 & 2 & 2 \\ \hline
Parité & pair & pair & pair & pair & pair & pair & pair & pair & pair & pair & pair & pair & pair & pair \\ \hline
\end{tabular}
\end{center}
\noindent\hspace{1.2em}Vérification : la somme de ces nombres vaut 44 = 2 \(\times\) 22, car chaque rue est comptée à ses \textbf{deux} extrémités.\par\addvspace{0.3em}
\noindent{\color{red!80!black}\bfseries \textbf{Aucun} carrefour n'a un nombre impair de rues : ils sont tous pairs.}\par\addvspace{0.4em}
\noindent \textbf{2.}\par\addvspace{0.35em}
\noindent{\color{green!45!black}\textbf{Le raisonnement clé.} Quand le facteur \textbf{traverse} un carrefour, il y arrive par une rue et en repart par une autre : il consomme les rues \textbf{deux par deux}. Un carrefour traversé 3 fois voit donc 6 de ses rues utilisées — toujours un nombre \textbf{pair}.}\par\addvspace{0.4em}
\noindent{\color{red!80!black}\bfseries Un carrefour où aboutit un nombre \textbf{impair} de rues ne peut donc pas être seulement traversé : il doit être le \textbf{départ} ou l'\textbf{arrivée} de la tournée. Là, une rue reste « non appariée ».}\par\addvspace{0.4em}
\noindent{\color{green!45!black}Ici la poste est \textbf{sur un carrefour}, en \textbf{S3}, et le facteur n'a pas à y revenir. Ce carrefour est donc le \textbf{départ} — il a droit d'être impair. Mais il n'y a qu'\textbf{une seule arrivée} : tous les autres carrefours doivent être pairs, sauf un au plus.}\par\addvspace{0.4em}
\noindent \textbf{3.}\par\addvspace{0.35em}
\noindent{\color{red!80!black}\bfseries \textbf{Oui.} Aucun carrefour n'est impair : chacun peut être traversé de part en part. Le facteur revient même à la poste sans l'avoir cherché.}\par\addvspace{0.4em}
\newpage
\noindent Voici une tournée possible — ce n'est pas la seule :\par\addvspace{0.35em}
\begin{enumerate}
  \item Il part de Rond-point du Pont \textbf{(S3)}, prend la \textbf{rue des Écoles ④} vers le nord et atteint Place Sainte-Croix \textbf{(S1)}.
  \item Il tourne à gauche dans la \textbf{rue de la Mairie ③}, vers l'ouest, jusqu'à Rond-point du Stade \textbf{(S2)}.
  \item Il continue tout droit dans l'\textbf{allée des Peupliers ①}, vers l'ouest, jusqu'à Place de l'Église \textbf{(S0)}.
  \item Il tourne à gauche dans le \textbf{chemin du Lavoir ②}, vers le sud, jusqu'à Carrefour du Moulin \textbf{(S4)}.
  \item Il tourne à gauche dans le \textbf{quai aux Fleurs ⑧}, vers le nord-est, jusqu'à Rond-point du Stade \textbf{(S2)}.
  \item Il tourne à droite dans la \textbf{rue du Stade ⑦}, vers le sud-est, jusqu'à Rond-point du Pont \textbf{(S3)}.
  \item Il tourne à droite dans la \textbf{rue des Jardins ⑨}, vers l'ouest, jusqu'à Carrefour du Moulin \textbf{(S4)}.
  \item Il tourne à gauche dans la \textbf{venelle du Chat ⑪}, vers le sud-est, jusqu'à Carrefour du Lavoir \textbf{(S5)}.
  \item Il tourne à droite dans le \textbf{passage du Marché ⑭}, vers le sud-ouest, jusqu'à Rond-point de la Poste \textbf{(S10)}.
  \item Il continue tout droit dans le \textbf{chemin Creux ⑤}, vers l'ouest, jusqu'à Fontaine Notre-Dame \textbf{(S13)}.
  \item Il tourne à droite dans la \textbf{rue Neuve ⑳}, vers le nord, jusqu'à Rond-point des Vaches \textbf{(S8)}.
  \item Il tourne à droite dans la \textbf{rue Pasteur ⑫}, vers le nord-est, jusqu'à Carrefour du Moulin \textbf{(S4)}.
  \item Il tourne à droite dans le \textbf{boulevard du Parc ⑬}, vers le sud, jusqu'à Carrefour Saint-Roch \textbf{(S9)}.
  \item Il tourne à droite dans l'\textbf{avenue de la Gare 21}, vers l'ouest, jusqu'à Rond-point des Vaches \textbf{(S8)}.
  \item Il tourne à gauche dans la \textbf{rue Verte ⑲}, vers le sud-est, jusqu'à Rond-point de la Poste \textbf{(S10)}.
  \item Il tourne à gauche dans la \textbf{rue du Four 22}, vers le nord-est, jusqu'à Carrefour Saint-Roch \textbf{(S9)}.
  \item Il tourne à droite dans le \textbf{chemin de Ronde ⑯}, vers l'est, jusqu'à Carrefour du Lavoir \textbf{(S5)}.
  \item Il tourne à droite dans la \textbf{rue de la Poste ⑮}, vers l'est, jusqu'à Coin du Lavoir \textbf{(S7)}.
  \item Il tourne à droite dans la \textbf{rue du Pont ⑱}, vers le sud, jusqu'à Place de la Fontaine \textbf{(S11)}.
  \item Il tourne à gauche dans la \textbf{rue du Moulin ⑥}, vers l'est, jusqu'à Placette des Ormes \textbf{(S12)}.
  \item Il tourne à gauche dans la \textbf{rue Haute ⑰}, vers le nord, jusqu'à Place des Tanneurs \textbf{(S6)}.
  \item Il tourne à gauche dans la \textbf{rue des Lilas ⑩}, vers le nord-ouest, jusqu'à Rond-point du Pont \textbf{(S3)}.
\end{enumerate}
\noindent \textbf{4.}\par\addvspace{0.35em}
\noindent{\color{red!80!black}\bfseries La question ne se pose pas : la tournée est possible au départ de la poste, et elle le resterait où qu'on installe celle-ci — aucun carrefour n'est impair.}\par\addvspace{0.4em}
\end{document}
