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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 G, 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 avenue de la Gare & \cellcolor{black!32}\bfseries Les carrefours & Ⓘ Place du Vieux-Puits \\ \hline
① rue du Puits & ⑩ chemin du Lavoir & Ⓐ Coin du Lavoir & Ⓙ Carrefour du Moulin \\ \hline
② rue du Pont & ⑪ rue de la Poste & Ⓑ Rond-point de la Gare & Ⓚ Carrefour de la Mairie \\ \hline
③ quai aux Fleurs & ⑫ sentier des Prés & Ⓒ Place des Tanneurs & Ⓛ Place de la Fontaine \\ \hline
④ rue de la Mairie & ⑬ chemin Creux & Ⓓ Carrefour du Lavoir & \cellcolor{black!32}\bfseries Les bâtiments \\ \hline
⑤ chemin de Ronde & ⑭ rue de l'Église & Ⓔ Rond-point des Vaches & \textbf{a} l'école \\ \hline
⑥ allée des Peupliers & ⑮ passage du Marché & Ⓕ Carrefour de l'Hôpital & \textbf{b} la salle des fêtes \\ \hline
⑦ boulevard du Parc & ⑯ rue des Lilas & Ⓖ Carrefour Saint-Roch & \textbf{c} la bibliothèque \\ \hline
⑧ rue Pasteur & ⑰ rue des Jardins & Ⓗ Rond-point du Stade & \textbf{d} le marché couvert \\ \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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\draw[line width=0.5pt] (8.537,4.873) -- (8.577,4.654) -- (8.612,4.433) -- (8.642,4.211) -- (8.667,3.989) -- (8.687,3.766) -- (8.701,3.543) -- (8.71,3.32) -- (8.714,3.096) -- (8.713,2.873) -- (8.706,2.649) -- (8.694,2.426) -- (8.677,2.203) -- (8.654,1.981) -- (8.627,1.759);
\draw[line width=0.5pt] (1.312,2.295) -- (1.545,2.246) -- (1.778,2.202) -- (2.013,2.164) -- (2.248,2.131) -- (2.484,2.104) -- (2.721,2.082) -- (2.958,2.066) -- (3.196,2.056) -- (3.434,2.051) -- (3.671,2.052) -- (3.909,2.058) -- (4.146,2.07) -- (4.383,2.087) -- (4.619,2.111);
\draw[line width=0.5pt] (4.619,2.111) -- (4.907,2.13) -- (5.195,2.142) -- (5.484,2.147) -- (5.773,2.145) -- (6.061,2.137) -- (6.35,2.122) -- (6.638,2.1) -- (6.925,2.071) -- (7.211,2.036) -- (7.497,1.994) -- (7.782,1.945) -- (8.065,1.89) -- (8.347,1.828) -- (8.627,1.759);
\draw[line width=0.5pt] (8.627,1.759) -- (8.811,1.713) -- (8.996,1.671) -- (9.182,1.634) -- (9.369,1.601) -- (9.557,1.573) -- (9.745,1.549) -- (9.934,1.529) -- (10.124,1.514) -- (10.314,1.504) -- (10.503,1.497) -- (10.693,1.496) -- (10.883,1.498) -- (11.073,1.506) -- (11.262,1.517);
\filldraw[fill=black!38, draw=black, line width=0.5pt] (2.61,8.704) -- (2.581,8.847) -- (2.5,8.968) -- (2.379,9.049) -- (2.237,9.077) -- (2.094,9.049) -- (1.973,8.968) -- (1.892,8.847) -- (1.863,8.704) -- (1.892,8.561) -- (1.973,8.44) -- (2.094,8.359) -- (2.237,8.331) -- (2.379,8.359) -- (2.5,8.44) -- (2.581,8.561) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (8.804,8.357) -- (8.775,8.5) -- (8.694,8.621) -- (8.573,8.702) -- (8.43,8.73) -- (8.288,8.702) -- (8.167,8.621) -- (8.086,8.5) -- (8.057,8.357) -- (8.086,8.214) -- (8.167,8.093) -- (8.288,8.012) -- (8.43,7.984) -- (8.573,8.012) -- (8.694,8.093) -- (8.775,8.214) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (11.509,8.172) -- (11.481,8.315) -- (11.4,8.436) -- (11.279,8.517) -- (11.136,8.546) -- (10.993,8.517) -- (10.872,8.436) -- (10.791,8.315) -- (10.763,8.172) -- (10.791,8.03) -- (10.872,7.909) -- (10.993,7.828) -- (11.136,7.799) -- (11.279,7.828) -- (11.4,7.909) -- (11.481,8.03) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (4.947,7.763) -- (4.918,7.906) -- (4.838,8.027) -- (4.716,8.108) -- (4.574,8.137) -- (4.431,8.108) -- (4.31,8.027) -- (4.229,7.906) -- (4.2,7.763) -- (4.229,7.621) -- (4.31,7.5) -- (4.431,7.419) -- (4.574,7.39) -- (4.716,7.419) -- (4.838,7.5) -- (4.918,7.621) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (11.686,5.159) -- (11.657,5.302) -- (11.576,5.423) -- (11.455,5.504) -- (11.312,5.532) -- (11.17,5.504) -- (11.049,5.423) -- (10.968,5.302) -- (10.939,5.159) -- (10.968,5.016) -- (11.049,4.895) -- (11.17,4.814) -- (11.312,4.786) -- (11.455,4.814) -- (11.576,4.895) -- (11.657,5.016) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (5.067,5.067) -- (5.038,5.21) -- (4.957,5.331) -- (4.836,5.412) -- (4.693,5.44) -- (4.551,5.412) -- (4.429,5.331) -- (4.349,5.21) -- (4.32,5.067) -- (4.349,4.924) -- (4.429,4.803) -- (4.551,4.722) -- (4.693,4.694) -- (4.836,4.722) -- (4.957,4.803) -- (5.038,4.924) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (1.841,4.964) -- (1.813,5.107) -- (1.732,5.228) -- (1.611,5.309) -- (1.468,5.337) -- (1.325,5.309) -- (1.204,5.228) -- (1.123,5.107) -- (1.095,4.964) -- (1.123,4.821) -- (1.204,4.7) -- (1.325,4.619) -- (1.468,4.591) -- (1.611,4.619) -- (1.732,4.7) -- (1.813,4.821) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (8.91,4.873) -- (8.881,5.016) -- (8.801,5.137) -- (8.679,5.218) -- (8.537,5.247) -- (8.394,5.218) -- (8.273,5.137) -- (8.192,5.016) -- (8.163,4.873) -- (8.192,4.731) -- (8.273,4.609) -- (8.394,4.529) -- (8.537,4.5) -- (8.679,4.529) -- (8.801,4.609) -- (8.881,4.731) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (1.686,2.295) -- (1.657,2.438) -- (1.576,2.559) -- (1.455,2.64) -- (1.312,2.668) -- (1.17,2.64) -- (1.049,2.559) -- (0.968,2.438) -- (0.939,2.295) -- (0.968,2.152) -- (1.049,2.031) -- (1.17,1.95) -- (1.312,1.922) -- (1.455,1.95) -- (1.576,2.031) -- (1.657,2.152) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (4.993,2.111) -- (4.964,2.253) -- (4.883,2.375) -- (4.762,2.455) -- (4.619,2.484) -- (4.477,2.455) -- (4.355,2.375) -- (4.275,2.253) -- (4.246,2.111) -- (4.275,1.968) -- (4.355,1.847) -- (4.477,1.766) -- (4.619,1.737) -- (4.762,1.766) -- (4.883,1.847) -- (4.964,1.968) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (9.0,1.759) -- (8.971,1.902) -- (8.891,2.023) -- (8.769,2.104) -- (8.627,2.132) -- (8.484,2.104) -- (8.363,2.023) -- (8.282,1.902) -- (8.253,1.759) -- (8.282,1.616) -- (8.363,1.495) -- (8.484,1.414) -- (8.627,1.386) -- (8.769,1.414) -- (8.891,1.495) -- (8.971,1.616) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (11.635,1.517) -- (11.607,1.66) -- (11.526,1.781) -- (11.405,1.862) -- (11.262,1.89) -- (11.119,1.862) -- (10.998,1.781) -- (10.917,1.66) -- (10.889,1.517) -- (10.917,1.374) -- (10.998,1.253) -- (11.119,1.172) -- (11.262,1.144) -- (11.405,1.172) -- (11.526,1.253) -- (11.607,1.374) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (3.223,7.396) -- (3.342,7.415) -- (3.449,7.469) -- (3.534,7.555) -- (3.588,7.662) -- (3.607,7.781) -- (3.588,7.899) -- (3.534,8.007) -- (3.449,8.092) -- (3.342,8.146) -- (3.223,8.165) -- (3.223,8.165) -- (3.104,8.146) -- (2.997,8.092) -- (2.912,8.007) -- (2.857,7.899) -- (2.838,7.781) -- (2.857,7.662) -- (2.912,7.555) -- (2.997,7.469) -- (3.104,7.415) -- (3.223,7.396) -- cycle;
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\filldraw[fill=white, draw=black, line width=0.5pt] (2.383,6.34) -- (2.502,6.359) -- (2.609,6.414) -- (2.694,6.499) -- (2.749,6.606) -- (2.768,6.725) -- (2.749,6.844) -- (2.694,6.951) -- (2.609,7.036) -- (2.502,7.091) -- (2.383,7.109) -- (2.383,7.109) -- (2.264,7.091) -- (2.157,7.036) -- (2.072,6.951) -- (2.018,6.844) -- (1.999,6.725) -- (2.018,6.606) -- (2.072,6.499) -- (2.157,6.414) -- (2.264,6.359) -- (2.383,6.34) -- cycle;
\node at (2.383,6.725) {\scalebox{1.609}{\small 2}};
\filldraw[fill=white, draw=black, line width=0.5pt] (9.802,8.152) -- (9.921,8.171) -- (10.028,8.226) -- (10.113,8.311) -- (10.167,8.418) -- (10.186,8.537) -- (10.167,8.656) -- (10.113,8.763) -- (10.028,8.848) -- (9.921,8.902) -- (9.802,8.921) -- (9.802,8.921) -- (9.683,8.902) -- (9.576,8.848) -- (9.491,8.763) -- (9.436,8.656) -- (9.417,8.537) -- (9.436,8.418) -- (9.491,8.311) -- (9.576,8.226) -- (9.683,8.171) -- (9.802,8.152) -- cycle;
\node at (9.802,8.537) {\scalebox{1.609}{\small 3}};
\filldraw[fill=white, draw=black, line width=0.5pt] (9.012,6.247) -- (9.13,6.266) -- (9.238,6.32) -- (9.323,6.405) -- (9.377,6.512) -- (9.396,6.631) -- (9.377,6.75) -- (9.323,6.857) -- (9.238,6.942) -- (9.13,6.997) -- (9.012,7.016) -- (9.012,7.016) -- (8.893,6.997) -- (8.786,6.942) -- (8.7,6.857) -- (8.646,6.75) -- (8.627,6.631) -- (8.646,6.512) -- (8.7,6.405) -- (8.786,6.32) -- (8.893,6.266) -- (9.012,6.247) -- cycle;
\node at (9.012,6.631) {\scalebox{1.609}{\small 4}};
\filldraw[fill=white, draw=black, line width=0.5pt] (11.484,6.296) -- (11.603,6.315) -- (11.71,6.37) -- (11.795,6.455) -- (11.849,6.562) -- (11.868,6.681) -- (11.849,6.8) -- (11.795,6.907) -- (11.71,6.992) -- (11.603,7.047) -- (11.484,7.065) -- (11.484,7.065) -- (11.365,7.047) -- (11.258,6.992) -- (11.173,6.907) -- (11.118,6.8) -- (11.099,6.681) -- (11.118,6.562) -- (11.173,6.455) -- (11.258,6.37) -- (11.365,6.315) -- (11.484,6.296) -- cycle;
\node at (11.484,6.681) {\scalebox{1.609}{\small 5}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.419,8.215) -- (6.538,8.234) -- (6.645,8.288) -- (6.73,8.373) -- (6.785,8.481) -- (6.804,8.599) -- (6.785,8.718) -- (6.73,8.825) -- (6.645,8.91) -- (6.538,8.965) -- (6.419,8.984) -- (6.419,8.984) -- (6.3,8.965) -- (6.193,8.91) -- (6.108,8.825) -- (6.053,8.718) -- (6.035,8.599) -- (6.053,8.481) -- (6.108,8.373) -- (6.193,8.288) -- (6.3,8.234) -- (6.419,8.215) -- cycle;
\node at (6.419,8.599) {\scalebox{1.609}{\small 6}};
\filldraw[fill=white, draw=black, line width=0.5pt] (4.906,6.043) -- (5.025,6.062) -- (5.132,6.116) -- (5.217,6.201) -- (5.272,6.308) -- (5.291,6.427) -- (5.272,6.546) -- (5.217,6.653) -- (5.132,6.738) -- (5.025,6.793) -- (4.906,6.812) -- (4.906,6.812) -- (4.788,6.793) -- (4.68,6.738) -- (4.595,6.653) -- (4.541,6.546) -- (4.522,6.427) -- (4.541,6.308) -- (4.595,6.201) -- (4.68,6.116) -- (4.788,6.062) -- (4.906,6.043) -- cycle;
\node at (4.906,6.427) {\scalebox{1.609}{\small 7}};
\filldraw[fill=white, draw=black, line width=0.5pt] (11.053,2.957) -- (11.172,2.976) -- (11.279,3.03) -- (11.364,3.115) -- (11.419,3.222) -- (11.438,3.341) -- (11.419,3.46) -- (11.364,3.567) -- (11.279,3.652) -- (11.172,3.707) -- (11.053,3.726) -- (11.053,3.726) -- (10.934,3.707) -- (10.827,3.652) -- (10.742,3.567) -- (10.687,3.46) -- (10.669,3.341) -- (10.687,3.222) -- (10.742,3.115) -- (10.827,3.03) -- (10.934,2.976) -- (11.053,2.957) -- cycle;
\node at (11.053,3.341) {\scalebox{1.609}{\small 8}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.626,4.811) -- (6.745,4.83) -- (6.852,4.885) -- (6.937,4.97) -- (6.992,5.077) -- (7.011,5.196) -- (6.992,5.314) -- (6.937,5.422) -- (6.852,5.507) -- (6.745,5.561) -- (6.626,5.58) -- (6.626,5.58) -- (6.508,5.561) -- (6.4,5.507) -- (6.315,5.422) -- (6.261,5.314) -- (6.242,5.196) -- (6.261,5.077) -- (6.315,4.97) -- (6.4,4.885) -- (6.508,4.83) -- (6.626,4.811) -- cycle;
\node at (6.626,5.196) {\scalebox{1.609}{\small 9}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.344,3.192) -- (5.462,3.21) -- (5.57,3.265) -- (5.655,3.35) -- (5.709,3.457) -- (5.728,3.576) -- (5.709,3.695) -- (5.655,3.802) -- (5.57,3.887) -- (5.462,3.942) -- (5.344,3.961) -- (4.982,3.961) -- (4.863,3.942) -- (4.756,3.887) -- (4.671,3.802) -- (4.616,3.695) -- (4.597,3.576) -- (4.616,3.457) -- (4.671,3.35) -- (4.756,3.265) -- (4.863,3.21) -- (4.982,3.192) -- cycle;
\node at (5.163,3.576) {\scalebox{1.609}{\small 10}};
\filldraw[fill=white, draw=black, line width=0.5pt] (3.278,4.114) -- (3.397,4.132) -- (3.504,4.187) -- (3.589,4.272) -- (3.644,4.379) -- (3.663,4.498) -- (3.644,4.617) -- (3.589,4.724) -- (3.504,4.809) -- (3.397,4.864) -- (3.278,4.883) -- (2.916,4.883) -- (2.797,4.864) -- (2.69,4.809) -- (2.605,4.724) -- (2.551,4.617) -- (2.532,4.498) -- (2.551,4.379) -- (2.605,4.272) -- (2.69,4.187) -- (2.797,4.132) -- (2.916,4.114) -- cycle;
\node at (3.097,4.498) {\scalebox{1.609}{\small 11}};
\filldraw[fill=white, draw=black, line width=0.5pt] (2.065,3.216) -- (2.184,3.235) -- (2.291,3.29) -- (2.376,3.375) -- (2.431,3.482) -- (2.45,3.601) -- (2.431,3.72) -- (2.376,3.827) -- (2.291,3.912) -- (2.184,3.966) -- (2.065,3.985) -- (1.703,3.985) -- (1.584,3.966) -- (1.477,3.912) -- (1.392,3.827) -- (1.338,3.72) -- (1.319,3.601) -- (1.338,3.482) -- (1.392,3.375) -- (1.477,3.29) -- (1.584,3.235) -- (1.703,3.216) -- cycle;
\node at (1.884,3.601) {\scalebox{1.609}{\small 12}};
\filldraw[fill=white, draw=black, line width=0.5pt] (10.457,4.948) -- (10.576,4.966) -- (10.683,5.021) -- (10.769,5.106) -- (10.823,5.213) -- (10.842,5.332) -- (10.823,5.451) -- (10.769,5.558) -- (10.683,5.643) -- (10.576,5.698) -- (10.457,5.717) -- (10.096,5.717) -- (9.977,5.698) -- (9.87,5.643) -- (9.784,5.558) -- (9.73,5.451) -- (9.711,5.332) -- (9.73,5.213) -- (9.784,5.106) -- (9.87,5.021) -- (9.977,4.966) -- (10.096,4.948) -- cycle;
\node at (10.276,5.332) {\scalebox{1.609}{\small 13}};
\filldraw[fill=white, draw=black, line width=0.5pt] (9.275,2.946) -- (9.394,2.965) -- (9.501,3.02) -- (9.587,3.105) -- (9.641,3.212) -- (9.66,3.331) -- (9.641,3.45) -- (9.587,3.557) -- (9.501,3.642) -- (9.394,3.697) -- (9.275,3.715) -- (8.914,3.715) -- (8.795,3.697) -- (8.688,3.642) -- (8.602,3.557) -- (8.548,3.45) -- (8.529,3.331) -- (8.548,3.212) -- (8.602,3.105) -- (8.688,3.02) -- (8.795,2.965) -- (8.914,2.946) -- cycle;
\node at (9.094,3.331) {\scalebox{1.609}{\small 14}};
\filldraw[fill=white, draw=black, line width=0.5pt] (3.161,2.066) -- (3.279,2.085) -- (3.387,2.139) -- (3.472,2.224) -- (3.526,2.331) -- (3.545,2.45) -- (3.526,2.569) -- (3.472,2.676) -- (3.387,2.761) -- (3.279,2.816) -- (3.161,2.835) -- (2.799,2.835) -- (2.68,2.816) -- (2.573,2.761) -- (2.488,2.676) -- (2.433,2.569) -- (2.414,2.45) -- (2.433,2.331) -- (2.488,2.224) -- (2.573,2.139) -- (2.68,2.085) -- (2.799,2.066) -- cycle;
\node at (2.98,2.45) {\scalebox{1.609}{\small 15}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.852,2.099) -- (6.971,2.117) -- (7.078,2.172) -- (7.163,2.257) -- (7.218,2.364) -- (7.237,2.483) -- (7.218,2.602) -- (7.163,2.709) -- (7.078,2.794) -- (6.971,2.849) -- (6.852,2.868) -- (6.49,2.868) -- (6.371,2.849) -- (6.264,2.794) -- (6.179,2.709) -- (6.124,2.602) -- (6.106,2.483) -- (6.124,2.364) -- (6.179,2.257) -- (6.264,2.172) -- (6.371,2.117) -- (6.49,2.099) -- cycle;
\node at (6.671,2.483) {\scalebox{1.609}{\small 16}};
\filldraw[fill=white, draw=black, line width=0.5pt] (10.151,1.528) -- (10.269,1.547) -- (10.377,1.601) -- (10.462,1.686) -- (10.516,1.793) -- (10.535,1.912) -- (10.516,2.031) -- (10.462,2.138) -- (10.377,2.223) -- (10.269,2.278) -- (10.151,2.297) -- (9.789,2.297) -- (9.67,2.278) -- (9.563,2.223) -- (9.478,2.138) -- (9.423,2.031) -- (9.404,1.912) -- (9.423,1.793) -- (9.478,1.686) -- (9.563,1.601) -- (9.67,1.547) -- (9.789,1.528) -- cycle;
\node at (9.97,1.912) {\scalebox{1.609}{\small 17}};
\filldraw[fill=yellow!35, draw=black, line width=0.5pt] (1.168,4.664) -- (1.768,4.664) -- (1.768,5.264) -- (1.168,5.264) -- cycle;
\node at (1.468,4.964) {\scalebox{1.609}{\small a}};
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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, B, E, F, I, K & 6 \\ \hline
clairs & C, D, G, H, J, L & 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 la \textbf{rue du Pont ②} vers le nord jusqu'à Coin du Lavoir \textbf{(A)}.\par\addvspace{0.35em}
\noindent Il tourne à droite dans la \textbf{rue du Puits ①}, vers l'est, jusqu'à Carrefour du Lavoir \textbf{(D)}.\par\addvspace{0.35em}
\noindent Il continue tout droit dans l'\textbf{allée des Peupliers ⑥}, vers l'est, jusqu'à Rond-point de la Gare \textbf{(B)}.\par\addvspace{0.35em}
\noindent Il continue tout droit dans le \textbf{quai aux Fleurs ③}, vers l'est, jusqu'à Place des Tanneurs \textbf{(C)}.\par\addvspace{0.35em}
\noindent Il tourne à droite dans le \textbf{chemin de Ronde ⑤}, vers le sud, jusqu'à Rond-point des Vaches \textbf{(E)}.\par\addvspace{0.35em}
\noindent Il continue tout droit dans la \textbf{rue Pasteur ⑧}, vers le sud, jusqu'à Place de la Fontaine \textbf{(L)}.\par\addvspace{0.35em}
\noindent Il tourne à droite dans la \textbf{rue des Jardins ⑰}, vers l'ouest, jusqu'à Carrefour de la Mairie \textbf{(K)}.\par\addvspace{0.35em}
\noindent Il tourne à droite dans la \textbf{rue de l'Église ⑭}, vers le nord, jusqu'à Rond-point du Stade \textbf{(H)}.\par\addvspace{0.35em}
\noindent Il tourne à gauche dans l'\textbf{avenue de la Gare ⑨}, vers l'ouest, jusqu'à Carrefour de l'Hôpital \textbf{(F)}.\par\addvspace{0.35em}
\noindent Il tourne à gauche dans le \textbf{chemin du Lavoir ⑩}, vers le sud, jusqu'à Carrefour du Moulin \textbf{(J)}.\par\addvspace{0.35em}
\noindent Il tourne à droite dans le \textbf{passage du Marché ⑮}, vers l'ouest, jusqu'à Place du Vieux-Puits \textbf{(I)}.\par\addvspace{0.35em}
\noindent Il tourne à droite dans le \textbf{sentier des Prés ⑫}, vers le nord, jusqu'à Carrefour Saint-Roch \textbf{(G)}.\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}
