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\newcommand{\titre}{Le car de ramassage}
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    \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.
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\end{center}
\noindent \textbf{Le car part de l'école, au carrefour J, et doit s'arrêter à chaque carrefour exactement une fois.} Il emprunte les rues qu'il veut et n'a pas à toutes les parcourir.\par\addvspace{0.35em}
\begin{center}
\renewcommand{\arraystretch}{1.35}
\begin{tabular}{|c|c|c|c|}
\hline
\cellcolor{black!32}\bfseries Les rues & ⑩ venelle du Chat & Ⓑ Fontaine Notre-Dame & Ⓛ Place de l'Église \\ \hline
① rue des Écoles & ⑪ rue Neuve & Ⓒ Place Sainte-Croix & Ⓜ Carrefour du Moulin \\ \hline
② rue de la Poste & ⑫ rue Basse & Ⓓ Carrefour de l'Hôpital & \cellcolor{black!32}\bfseries Les bâtiments \\ \hline
③ chemin Creux & ⑬ rue de l'Église & Ⓔ Carrefour de la Mairie & \textbf{a} l'école \\ \hline
④ rue Pasteur & ⑭ rue du Stade & Ⓕ Place du Marché & \textbf{b} le gymnase \\ \hline
⑤ rue Haute & ⑮ allée des Tilleuls & Ⓖ Place de la Fontaine & \textbf{c} le lavoir \\ \hline
⑥ rue du Puits & ⑯ impasse Sainte-Anne & Ⓗ Carrefour Saint-Roch & \textbf{d} la gendarmerie \\ \hline
⑦ chemin de Ronde & ⑰ sentier des Prés & Ⓘ Rond-point de la Poste &  \\ \hline
⑧ avenue de la Gare & \cellcolor{black!32}\bfseries Les carrefours & Ⓙ Rond-point de la Gare &  \\ \hline
⑨ boulevard du Parc & Ⓐ Carrefour des Tilleuls & Ⓚ Place aux Herbes &  \\ \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}
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\filldraw[fill=black!38, draw=black, line width=0.5pt] (4.232,11.536) -- (4.203,11.678) -- (4.122,11.799) -- (4.001,11.88) -- (3.859,11.909) -- (3.716,11.88) -- (3.595,11.799) -- (3.514,11.678) -- (3.485,11.536) -- (3.514,11.393) -- (3.595,11.272) -- (3.716,11.191) -- (3.859,11.162) -- (4.001,11.191) -- (4.122,11.272) -- (4.203,11.393) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (7.985,11.353) -- (7.957,11.496) -- (7.876,11.617) -- (7.755,11.698) -- (7.612,11.726) -- (7.469,11.698) -- (7.348,11.617) -- (7.267,11.496) -- (7.239,11.353) -- (7.267,11.21) -- (7.348,11.089) -- (7.469,11.008) -- (7.612,10.98) -- (7.755,11.008) -- (7.876,11.089) -- (7.957,11.21) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (1.596,11.278) -- (1.567,11.421) -- (1.486,11.542) -- (1.365,11.623) -- (1.222,11.652) -- (1.08,11.623) -- (0.958,11.542) -- (0.878,11.421) -- (0.849,11.278) -- (0.878,11.136) -- (0.958,11.015) -- (1.08,10.934) -- (1.222,10.905) -- (1.365,10.934) -- (1.486,11.015) -- (1.567,11.136) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (4.919,8.893) -- (4.89,9.036) -- (4.809,9.157) -- (4.688,9.238) -- (4.545,9.266) -- (4.403,9.238) -- (4.281,9.157) -- (4.201,9.036) -- (4.172,8.893) -- (4.201,8.75) -- (4.281,8.629) -- (4.403,8.548) -- (4.545,8.52) -- (4.688,8.548) -- (4.809,8.629) -- (4.89,8.75) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (7.701,8.764) -- (7.673,8.907) -- (7.592,9.028) -- (7.471,9.109) -- (7.328,9.137) -- (7.185,9.109) -- (7.064,9.028) -- (6.983,8.907) -- (6.955,8.764) -- (6.983,8.621) -- (7.064,8.5) -- (7.185,8.419) -- (7.328,8.391) -- (7.471,8.419) -- (7.592,8.5) -- (7.673,8.621) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (1.694,8.71) -- (1.665,8.853) -- (1.584,8.974) -- (1.463,9.054) -- (1.32,9.083) -- (1.178,9.054) -- (1.057,8.974) -- (0.976,8.853) -- (0.947,8.71) -- (0.976,8.567) -- (1.057,8.446) -- (1.178,8.365) -- (1.32,8.336) -- (1.463,8.365) -- (1.584,8.446) -- (1.665,8.567) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (10.91,5.426) -- (10.881,5.568) -- (10.801,5.69) -- (10.679,5.77) -- (10.537,5.799) -- (10.394,5.77) -- (10.273,5.69) -- (10.192,5.568) -- (10.163,5.426) -- (10.192,5.283) -- (10.273,5.162) -- (10.394,5.081) -- (10.537,5.052) -- (10.679,5.081) -- (10.801,5.162) -- (10.881,5.283) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (7.649,5.184) -- (7.621,5.326) -- (7.54,5.448) -- (7.419,5.528) -- (7.276,5.557) -- (7.133,5.528) -- (7.012,5.448) -- (6.931,5.326) -- (6.903,5.184) -- (6.931,5.041) -- (7.012,4.92) -- (7.133,4.839) -- (7.276,4.81) -- (7.419,4.839) -- (7.54,4.92) -- (7.621,5.041) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (4.294,4.977) -- (4.265,5.12) -- (4.184,5.241) -- (4.063,5.322) -- (3.92,5.35) -- (3.778,5.322) -- (3.656,5.241) -- (3.576,5.12) -- (3.547,4.977) -- (3.576,4.834) -- (3.656,4.713) -- (3.778,4.632) -- (3.92,4.604) -- (4.063,4.632) -- (4.184,4.713) -- (4.265,4.834) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (7.655,2.233) -- (7.627,2.376) -- (7.546,2.497) -- (7.425,2.578) -- (7.282,2.606) -- (7.139,2.578) -- (7.018,2.497) -- (6.937,2.376) -- (6.909,2.233) -- (6.937,2.09) -- (7.018,1.969) -- (7.139,1.888) -- (7.282,1.86) -- (7.425,1.888) -- (7.546,1.969) -- (7.627,2.09) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (1.572,2.192) -- (1.544,2.334) -- (1.463,2.456) -- (1.342,2.536) -- (1.199,2.565) -- (1.056,2.536) -- (0.935,2.456) -- (0.854,2.334) -- (0.826,2.192) -- (0.854,2.049) -- (0.935,1.928) -- (1.056,1.847) -- (1.199,1.818) -- (1.342,1.847) -- (1.463,1.928) -- (1.544,2.049) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (10.778,2.124) -- (10.75,2.267) -- (10.669,2.388) -- (10.548,2.469) -- (10.405,2.498) -- (10.262,2.469) -- (10.141,2.388) -- (10.06,2.267) -- (10.032,2.124) -- (10.06,1.982) -- (10.141,1.86) -- (10.262,1.78) -- (10.405,1.751) -- (10.548,1.78) -- (10.669,1.86) -- (10.75,1.982) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (4.051,1.536) -- (4.023,1.678) -- (3.942,1.799) -- (3.821,1.88) -- (3.678,1.909) -- (3.535,1.88) -- (3.414,1.799) -- (3.333,1.678) -- (3.305,1.536) -- (3.333,1.393) -- (3.414,1.272) -- (3.535,1.191) -- (3.678,1.162) -- (3.821,1.191) -- (3.942,1.272) -- (4.023,1.393) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (5.747,11.289) -- (5.865,11.308) -- (5.973,11.363) -- (6.058,11.448) -- (6.112,11.555) -- (6.131,11.674) -- (6.112,11.792) -- (6.058,11.9) -- (5.973,11.985) -- (5.865,12.039) -- (5.747,12.058) -- (5.747,12.058) -- (5.628,12.039) -- (5.52,11.985) -- (5.435,11.9) -- (5.381,11.792) -- (5.362,11.674) -- (5.381,11.555) -- (5.435,11.448) -- (5.52,11.363) -- (5.628,11.308) -- (5.747,11.289) -- cycle;
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\filldraw[fill=white, draw=black, line width=0.5pt] (4.683,9.955) -- (4.802,9.974) -- (4.909,10.028) -- (4.994,10.113) -- (5.049,10.22) -- (5.068,10.339) -- (5.049,10.458) -- (4.994,10.565) -- (4.909,10.65) -- (4.802,10.705) -- (4.683,10.724) -- (4.683,10.724) -- (4.564,10.705) -- (4.457,10.65) -- (4.372,10.565) -- (4.317,10.458) -- (4.299,10.339) -- (4.317,10.22) -- (4.372,10.113) -- (4.457,10.028) -- (4.564,9.974) -- (4.683,9.955) -- cycle;
\node at (4.683,10.339) {\scalebox{1.517}{\small 2}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.981,9.728) -- (7.1,9.747) -- (7.207,9.801) -- (7.292,9.886) -- (7.347,9.994) -- (7.366,10.112) -- (7.347,10.231) -- (7.292,10.338) -- (7.207,10.424) -- (7.1,10.478) -- (6.981,10.497) -- (6.981,10.497) -- (6.862,10.478) -- (6.755,10.424) -- (6.67,10.338) -- (6.615,10.231) -- (6.596,10.112) -- (6.615,9.994) -- (6.67,9.886) -- (6.755,9.801) -- (6.862,9.747) -- (6.981,9.728) -- cycle;
\node at (6.981,10.112) {\scalebox{1.517}{\small 3}};
\filldraw[fill=white, draw=black, line width=0.5pt] (2.493,11.514) -- (2.611,11.533) -- (2.719,11.587) -- (2.804,11.672) -- (2.858,11.78) -- (2.877,11.898) -- (2.858,12.017) -- (2.804,12.124) -- (2.719,12.21) -- (2.611,12.264) -- (2.493,12.283) -- (2.493,12.283) -- (2.374,12.264) -- (2.267,12.21) -- (2.181,12.124) -- (2.127,12.017) -- (2.108,11.898) -- (2.127,11.78) -- (2.181,11.672) -- (2.267,11.587) -- (2.374,11.533) -- (2.493,11.514) -- cycle;
\node at (2.493,11.898) {\scalebox{1.517}{\small 4}};
\filldraw[fill=white, draw=black, line width=0.5pt] (1.55,9.62) -- (1.668,9.639) -- (1.776,9.694) -- (1.861,9.779) -- (1.915,9.886) -- (1.934,10.005) -- (1.915,10.124) -- (1.861,10.231) -- (1.776,10.316) -- (1.668,10.37) -- (1.55,10.389) -- (1.55,10.389) -- (1.431,10.37) -- (1.324,10.316) -- (1.239,10.231) -- (1.184,10.124) -- (1.165,10.005) -- (1.184,9.886) -- (1.239,9.779) -- (1.324,9.694) -- (1.431,9.639) -- (1.55,9.62) -- cycle;
\node at (1.55,10.005) {\scalebox{1.517}{\small 5}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.96,8.943) -- (6.078,8.962) -- (6.186,9.016) -- (6.271,9.101) -- (6.325,9.209) -- (6.344,9.327) -- (6.325,9.446) -- (6.271,9.553) -- (6.186,9.638) -- (6.078,9.693) -- (5.96,9.712) -- (5.96,9.712) -- (5.841,9.693) -- (5.734,9.638) -- (5.649,9.553) -- (5.594,9.446) -- (5.575,9.327) -- (5.594,9.209) -- (5.649,9.101) -- (5.734,9.016) -- (5.841,8.962) -- (5.96,8.943) -- cycle;
\node at (5.96,9.327) {\scalebox{1.517}{\small 6}};
\filldraw[fill=white, draw=black, line width=0.5pt] (4.451,6.516) -- (4.57,6.534) -- (4.677,6.589) -- (4.762,6.674) -- (4.817,6.781) -- (4.836,6.9) -- (4.817,7.019) -- (4.762,7.126) -- (4.677,7.211) -- (4.57,7.266) -- (4.451,7.285) -- (4.451,7.285) -- (4.332,7.266) -- (4.225,7.211) -- (4.14,7.126) -- (4.085,7.019) -- (4.066,6.9) -- (4.085,6.781) -- (4.14,6.674) -- (4.225,6.589) -- (4.332,6.534) -- (4.451,6.516) -- cycle;
\node at (4.451,6.9) {\scalebox{1.517}{\small 7}};
\filldraw[fill=white, draw=black, line width=0.5pt] (7.834,6.582) -- (7.953,6.6) -- (8.06,6.655) -- (8.145,6.74) -- (8.2,6.847) -- (8.219,6.966) -- (8.2,7.085) -- (8.145,7.192) -- (8.06,7.277) -- (7.953,7.332) -- (7.834,7.351) -- (7.834,7.351) -- (7.715,7.332) -- (7.608,7.277) -- (7.523,7.192) -- (7.468,7.085) -- (7.45,6.966) -- (7.468,6.847) -- (7.523,6.74) -- (7.608,6.655) -- (7.715,6.6) -- (7.834,6.582) -- cycle;
\node at (7.834,6.966) {\scalebox{1.517}{\small 8}};
\filldraw[fill=white, draw=black, line width=0.5pt] (2.919,8.668) -- (3.037,8.686) -- (3.145,8.741) -- (3.23,8.826) -- (3.284,8.933) -- (3.303,9.052) -- (3.284,9.171) -- (3.23,9.278) -- (3.145,9.363) -- (3.037,9.418) -- (2.919,9.437) -- (2.919,9.437) -- (2.8,9.418) -- (2.693,9.363) -- (2.608,9.278) -- (2.553,9.171) -- (2.534,9.052) -- (2.553,8.933) -- (2.608,8.826) -- (2.693,8.741) -- (2.8,8.686) -- (2.919,8.668) -- cycle;
\node at (2.919,9.052) {\scalebox{1.517}{\small 9}};
\filldraw[fill=white, draw=black, line width=0.5pt] (11.172,3.37) -- (11.291,3.389) -- (11.398,3.443) -- (11.483,3.528) -- (11.538,3.635) -- (11.557,3.754) -- (11.538,3.873) -- (11.483,3.98) -- (11.398,4.065) -- (11.291,4.12) -- (11.172,4.139) -- (10.81,4.139) -- (10.691,4.12) -- (10.584,4.065) -- (10.499,3.98) -- (10.445,3.873) -- (10.426,3.754) -- (10.445,3.635) -- (10.499,3.528) -- (10.584,3.443) -- (10.691,3.389) -- (10.81,3.37) -- cycle;
\node at (10.991,3.754) {\scalebox{1.517}{\small 10}};
\filldraw[fill=white, draw=black, line width=0.5pt] (9.069,5.169) -- (9.188,5.188) -- (9.295,5.243) -- (9.38,5.328) -- (9.435,5.435) -- (9.453,5.554) -- (9.435,5.672) -- (9.38,5.78) -- (9.295,5.865) -- (9.188,5.919) -- (9.069,5.938) -- (8.707,5.938) -- (8.588,5.919) -- (8.481,5.865) -- (8.396,5.78) -- (8.341,5.672) -- (8.322,5.554) -- (8.341,5.435) -- (8.396,5.328) -- (8.481,5.243) -- (8.588,5.188) -- (8.707,5.169) -- cycle;
\node at (8.888,5.554) {\scalebox{1.517}{\small 11}};
\filldraw[fill=white, draw=black, line width=0.5pt] (7.966,3.325) -- (8.085,3.344) -- (8.192,3.398) -- (8.277,3.483) -- (8.332,3.591) -- (8.351,3.709) -- (8.332,3.828) -- (8.277,3.935) -- (8.192,4.02) -- (8.085,4.075) -- (7.966,4.094) -- (7.604,4.094) -- (7.486,4.075) -- (7.378,4.02) -- (7.293,3.935) -- (7.239,3.828) -- (7.22,3.709) -- (7.239,3.591) -- (7.293,3.483) -- (7.378,3.398) -- (7.486,3.344) -- (7.604,3.325) -- cycle;
\node at (7.785,3.709) {\scalebox{1.517}{\small 12}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.764,4.941) -- (5.883,4.96) -- (5.99,5.015) -- (6.075,5.1) -- (6.13,5.207) -- (6.149,5.326) -- (6.13,5.444) -- (6.075,5.552) -- (5.99,5.637) -- (5.883,5.691) -- (5.764,5.71) -- (5.402,5.71) -- (5.283,5.691) -- (5.176,5.637) -- (5.091,5.552) -- (5.036,5.444) -- (5.018,5.326) -- (5.036,5.207) -- (5.091,5.1) -- (5.176,5.015) -- (5.283,4.96) -- (5.402,4.941) -- cycle;
\node at (5.583,5.326) {\scalebox{1.517}{\small 13}};
\filldraw[fill=white, draw=black, line width=0.5pt] (4.506,2.835) -- (4.624,2.853) -- (4.732,2.908) -- (4.817,2.993) -- (4.871,3.1) -- (4.89,3.219) -- (4.871,3.338) -- (4.817,3.445) -- (4.732,3.53) -- (4.624,3.585) -- (4.506,3.604) -- (4.144,3.604) -- (4.025,3.585) -- (3.918,3.53) -- (3.833,3.445) -- (3.778,3.338) -- (3.759,3.219) -- (3.778,3.1) -- (3.833,2.993) -- (3.918,2.908) -- (4.025,2.853) -- (4.144,2.835) -- cycle;
\node at (4.325,3.219) {\scalebox{1.517}{\small 14}};
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\noindent{\small\itshape Deux carrefours reliés par une rue n'ont jamais la même couleur.}\par\addvspace{0.4em}
\noindent \textbf{1.} Le coloriage est \textbf{forcé} : une fois la couleur d'un carrefour choisie, celle de tous les autres suit, de proche en proche.\par\addvspace{0.35em}
\begin{center}
\renewcommand{\arraystretch}{1.35}
\begin{tabular}{|c|c|c|}
\hline
\cellcolor{blue!7}\bfseries Couleur & \cellcolor{blue!7}\bfseries Carrefours & \cellcolor{blue!7}\bfseries Nombre \\ \hline
sombres & A, E, F, G, I, J, K & 7 \\ \hline
clairs & B, C, D, H, L, M & 6 \\ \hline
\end{tabular}
\end{center}
\noindent{\color{red!80!black}\bfseries Il y a \textbf{7} carrefours sombres et \textbf{6} clairs. Il y en a donc \textbf{1 de plus} du côté des sombres.}\par\addvspace{0.4em}
\noindent \textbf{2.}\par\addvspace{0.35em}
\noindent{\color{green!45!black}\textbf{Le raisonnement clé.} Chaque rue relie un carrefour sombre à un carrefour clair. Donc à chaque fois que le car roule, il \textbf{change de couleur} : ses arrêts sont sombre, clair, sombre, clair\dots{} \textbf{en alternance}.}\par\addvspace{0.4em}
\noindent{\color{red!80!black}\bfseries Une tournée qui dessert les 13 carrefours alterne donc les deux couleurs d'un bout à l'autre : elle en utilise \textbf{autant de chaque, à un près}. Et si elle en utilise un de plus d'une couleur, c'est forcément celle de son \textbf{départ} et de son \textbf{arrivée}.}\par\addvspace{0.4em}
\noindent \textbf{3.}\par\addvspace{0.35em}
\noindent{\color{red!80!black}\bfseries \textbf{Non.} Un circuit revient à son point de départ : il compte autant d'arrêts sombres que de clairs. Or ce quartier a 7 carrefours sombres et 6 clairs — c'est impossible.}\par\addvspace{0.4em}
\noindent \textbf{4.}\par\addvspace{0.35em}
\noindent{\color{red!80!black}\bfseries \textbf{Oui}, à condition de ne pas revenir. Un trajet possible au départ de \textbf{J} :}\par\addvspace{0.4em}
\newpage
\noindent \textbf{Le trajet du car}\par\addvspace{0.35em}
\noindent Le car sort de l'école et prend l'\textbf{allée des Tilleuls ⑮} vers l'est jusqu'à Place de l'Église \textbf{(L)}.\par\addvspace{0.35em}
\noindent Il tourne à gauche dans la \textbf{venelle du Chat ⑩}, vers le nord, jusqu'à Place de la Fontaine \textbf{(G)}.\par\addvspace{0.35em}
\noindent Il tourne à gauche dans la \textbf{rue Neuve ⑪}, vers l'ouest, jusqu'à Carrefour Saint-Roch \textbf{(H)}.\par\addvspace{0.35em}
\noindent Il tourne à droite dans l'\textbf{avenue de la Gare ⑧}, vers le nord, jusqu'à Carrefour de la Mairie \textbf{(E)}.\par\addvspace{0.35em}
\noindent Il continue tout droit dans le \textbf{chemin Creux ③}, vers le nord, jusqu'à Fontaine Notre-Dame \textbf{(B)}.\par\addvspace{0.35em}
\noindent Il tourne à gauche dans la \textbf{rue des Écoles ①}, vers l'ouest, jusqu'à Carrefour des Tilleuls \textbf{(A)}.\par\addvspace{0.35em}
\noindent Il continue tout droit dans la \textbf{rue Pasteur ④}, vers l'ouest, jusqu'à Place Sainte-Croix \textbf{(C)}.\par\addvspace{0.35em}
\noindent Il tourne à gauche dans la \textbf{rue Haute ⑤}, vers le sud, jusqu'à Place du Marché \textbf{(F)}.\par\addvspace{0.35em}
\noindent Il tourne à gauche dans le \textbf{boulevard du Parc ⑨}, vers l'est, jusqu'à Carrefour de l'Hôpital \textbf{(D)}.\par\addvspace{0.35em}
\noindent Il tourne à droite dans le \textbf{chemin de Ronde ⑦}, vers le sud, jusqu'à Rond-point de la Poste \textbf{(I)}.\par\addvspace{0.35em}
\noindent Il continue tout droit dans la \textbf{rue du Stade ⑭}, vers le sud, jusqu'à Carrefour du Moulin \textbf{(M)}.\par\addvspace{0.35em}
\noindent Il tourne à droite dans l'\textbf{impasse Sainte-Anne ⑯}, vers l'ouest, jusqu'à Place aux Herbes \textbf{(K)}.\par\addvspace{0.35em}
\noindent{\color{red!80!black}\bfseries Les 13 carrefours ont été desservis une fois chacun. Le car termine loin de l'école : c'est permis ici, mais pas à la question 3.}\par\addvspace{0.4em}
\end{document}
