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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 K, 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 chemin de Ronde & \cellcolor{black!32}\bfseries Les carrefours & Ⓘ Place du Marché \\ \hline
① rue Haute & ⑩ rue Neuve & Ⓐ Place des Tanneurs & Ⓙ Coin du Lavoir \\ \hline
② allée des Peupliers & ⑪ sentier des Prés & Ⓑ Placette des Ormes & Ⓚ Rond-point de la Poste \\ \hline
③ rue du Stade & ⑫ chemin du Lavoir & Ⓒ Carrefour de la Mairie & Ⓛ Rond-point de la Gare \\ \hline
④ chemin des Vignes & ⑬ rue du Pont & Ⓓ Rond-point du Pont & \cellcolor{black!32}\bfseries Les bâtiments \\ \hline
⑤ passage du Marché & ⑭ rue du Four & Ⓔ Carrefour du Moulin & \textbf{a} l'école \\ \hline
⑥ rue Basse & ⑮ rue des Écoles & Ⓕ Rond-point du Stade & \textbf{b} la mairie \\ \hline
⑦ rue du Puits & ⑯ quai aux Fleurs & Ⓖ Carrefour du Lavoir & \textbf{c} le lavoir \\ \hline
⑧ avenue de la Gare & ⑰ chemin Creux & Ⓗ Carrefour de l'Hôpital & \textbf{d} la bibliothèque \\ \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] (1.792,2.296) -- (1.971,2.211) -- (2.152,2.129) -- (2.334,2.052) -- (2.519,1.98) -- (2.705,1.911) -- (2.893,1.848) -- (3.083,1.788) -- (3.273,1.733) -- (3.465,1.683) -- (3.658,1.637) -- (3.852,1.595) -- (4.047,1.558) -- (4.243,1.526) -- (4.439,1.499);
\draw[line width=0.5pt] (8.198,1.893) -- (8.386,1.964) -- (8.576,2.031) -- (8.767,2.093) -- (8.96,2.15) -- (9.153,2.203) -- (9.349,2.252) -- (9.545,2.295) -- (9.742,2.335) -- (9.94,2.369) -- (10.139,2.399) -- (10.338,2.424) -- (10.538,2.445) -- (10.739,2.46) -- (10.939,2.471);
\draw[line width=0.5pt] (4.439,1.499) -- (4.71,1.486) -- (4.981,1.479) -- (5.252,1.478) -- (5.523,1.485) -- (5.794,1.497) -- (6.065,1.516) -- (6.335,1.541) -- (6.604,1.572) -- (6.873,1.61) -- (7.141,1.654) -- (7.407,1.705) -- (7.672,1.761) -- (7.936,1.824) -- (8.198,1.893);
\filldraw[fill=black!38, draw=black, line width=0.5pt] (1.648,8.633) -- (1.619,8.776) -- (1.538,8.897) -- (1.417,8.978) -- (1.275,9.006) -- (1.132,8.978) -- (1.011,8.897) -- (0.93,8.776) -- (0.901,8.633) -- (0.93,8.49) -- (1.011,8.369) -- (1.132,8.288) -- (1.275,8.26) -- (1.417,8.288) -- (1.538,8.369) -- (1.619,8.49) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (11.648,8.456) -- (11.619,8.599) -- (11.538,8.72) -- (11.417,8.801) -- (11.275,8.83) -- (11.132,8.801) -- (11.011,8.72) -- (10.93,8.599) -- (10.901,8.456) -- (10.93,8.313) -- (11.011,8.192) -- (11.132,8.112) -- (11.275,8.083) -- (11.417,8.112) -- (11.538,8.192) -- (11.619,8.313) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (5.548,8.156) -- (5.519,8.299) -- (5.438,8.42) -- (5.317,8.501) -- (5.174,8.529) -- (5.032,8.501) -- (4.91,8.42) -- (4.83,8.299) -- (4.801,8.156) -- (4.83,8.013) -- (4.91,7.892) -- (5.032,7.811) -- (5.174,7.783) -- (5.317,7.811) -- (5.438,7.892) -- (5.519,8.013) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (8.845,8.118) -- (8.817,8.261) -- (8.736,8.382) -- (8.615,8.463) -- (8.472,8.491) -- (8.329,8.463) -- (8.208,8.382) -- (8.127,8.261) -- (8.099,8.118) -- (8.127,7.975) -- (8.208,7.854) -- (8.329,7.773) -- (8.472,7.745) -- (8.615,7.773) -- (8.736,7.854) -- (8.817,7.975) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (2.139,5.244) -- (2.11,5.386) -- (2.03,5.507) -- (1.908,5.588) -- (1.766,5.617) -- (1.623,5.588) -- (1.502,5.507) -- (1.421,5.386) -- (1.392,5.244) -- (1.421,5.101) -- (1.502,4.98) -- (1.623,4.899) -- (1.766,4.87) -- (1.908,4.899) -- (2.03,4.98) -- (2.11,5.101) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (10.994,5.229) -- (10.966,5.372) -- (10.885,5.493) -- (10.764,5.574) -- (10.621,5.603) -- (10.478,5.574) -- (10.357,5.493) -- (10.276,5.372) -- (10.248,5.229) -- (10.276,5.087) -- (10.357,4.965) -- (10.478,4.885) -- (10.621,4.856) -- (10.764,4.885) -- (10.885,4.965) -- (10.966,5.087) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (4.956,4.795) -- (4.927,4.937) -- (4.847,5.058) -- (4.725,5.139) -- (4.583,5.168) -- (4.44,5.139) -- (4.319,5.058) -- (4.238,4.937) -- (4.209,4.795) -- (4.238,4.652) -- (4.319,4.531) -- (4.44,4.45) -- (4.583,4.421) -- (4.725,4.45) -- (4.847,4.531) -- (4.927,4.652) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (7.965,4.647) -- (7.936,4.79) -- (7.855,4.911) -- (7.734,4.992) -- (7.592,5.021) -- (7.449,4.992) -- (7.328,4.911) -- (7.247,4.79) -- (7.218,4.647) -- (7.247,4.505) -- (7.328,4.384) -- (7.449,4.303) -- (7.592,4.274) -- (7.734,4.303) -- (7.855,4.384) -- (7.936,4.505) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (11.312,2.471) -- (11.284,2.614) -- (11.203,2.735) -- (11.082,2.816) -- (10.939,2.844) -- (10.796,2.816) -- (10.675,2.735) -- (10.594,2.614) -- (10.566,2.471) -- (10.594,2.328) -- (10.675,2.207) -- (10.796,2.126) -- (10.939,2.098) -- (11.082,2.126) -- (11.203,2.207) -- (11.284,2.328) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (2.165,2.296) -- (2.137,2.439) -- (2.056,2.56) -- (1.935,2.641) -- (1.792,2.669) -- (1.649,2.641) -- (1.528,2.56) -- (1.447,2.439) -- (1.419,2.296) -- (1.447,2.153) -- (1.528,2.032) -- (1.649,1.951) -- (1.792,1.923) -- (1.935,1.951) -- (2.056,2.032) -- (2.137,2.153) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (8.571,1.893) -- (8.543,2.036) -- (8.462,2.157) -- (8.341,2.238) -- (8.198,2.267) -- (8.055,2.238) -- (7.934,2.157) -- (7.853,2.036) -- (7.825,1.893) -- (7.853,1.751) -- (7.934,1.63) -- (8.055,1.549) -- (8.198,1.52) -- (8.341,1.549) -- (8.462,1.63) -- (8.543,1.751) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (4.812,1.499) -- (4.784,1.642) -- (4.703,1.763) -- (4.582,1.844) -- (4.439,1.872) -- (4.296,1.844) -- (4.175,1.763) -- (4.094,1.642) -- (4.066,1.499) -- (4.094,1.356) -- (4.175,1.235) -- (4.296,1.154) -- (4.439,1.126) -- (4.582,1.154) -- (4.703,1.235) -- (4.784,1.356) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (3.251,8.231) -- (3.37,8.25) -- (3.477,8.304) -- (3.563,8.389) -- (3.617,8.496) -- (3.636,8.615) -- (3.617,8.734) -- (3.563,8.841) -- (3.477,8.926) -- (3.37,8.981) -- (3.251,9.0) -- (3.251,9.0) -- (3.133,8.981) -- (3.025,8.926) -- (2.94,8.841) -- (2.886,8.734) -- (2.867,8.615) -- (2.886,8.496) -- (2.94,8.389) -- (3.025,8.304) -- (3.133,8.25) -- (3.251,8.231) -- cycle;
\node at (3.251,8.615) {\scalebox{1.604}{\small 1}};
\filldraw[fill=white, draw=black, line width=0.5pt] (2.04,6.629) -- (2.159,6.648) -- (2.266,6.703) -- (2.352,6.788) -- (2.406,6.895) -- (2.425,7.014) -- (2.406,7.132) -- (2.352,7.24) -- (2.266,7.325) -- (2.159,7.379) -- (2.04,7.398) -- (2.04,7.398) -- (1.922,7.379) -- (1.814,7.325) -- (1.729,7.24) -- (1.675,7.132) -- (1.656,7.014) -- (1.675,6.895) -- (1.729,6.788) -- (1.814,6.703) -- (1.922,6.648) -- (2.04,6.629) -- cycle;
\node at (2.04,7.014) {\scalebox{1.604}{\small 2}};
\filldraw[fill=white, draw=black, line width=0.5pt] (11.192,6.409) -- (11.31,6.428) -- (11.418,6.482) -- (11.503,6.567) -- (11.557,6.675) -- (11.576,6.793) -- (11.557,6.912) -- (11.503,7.019) -- (11.418,7.105) -- (11.31,7.159) -- (11.192,7.178) -- (11.192,7.178) -- (11.073,7.159) -- (10.966,7.105) -- (10.881,7.019) -- (10.826,6.912) -- (10.807,6.793) -- (10.826,6.675) -- (10.881,6.567) -- (10.966,6.482) -- (11.073,6.428) -- (11.192,6.409) -- cycle;
\node at (11.192,6.793) {\scalebox{1.604}{\small 3}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.829,8.273) -- (6.948,8.292) -- (7.055,8.346) -- (7.14,8.431) -- (7.195,8.539) -- (7.214,8.658) -- (7.195,8.776) -- (7.14,8.884) -- (7.055,8.969) -- (6.948,9.023) -- (6.829,9.042) -- (6.829,9.042) -- (6.71,9.023) -- (6.603,8.969) -- (6.518,8.884) -- (6.464,8.776) -- (6.445,8.658) -- (6.464,8.539) -- (6.518,8.431) -- (6.603,8.346) -- (6.71,8.292) -- (6.829,8.273) -- cycle;
\node at (6.829,8.658) {\scalebox{1.604}{\small 4}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.119,6.049) -- (5.237,6.067) -- (5.345,6.122) -- (5.43,6.207) -- (5.484,6.314) -- (5.503,6.433) -- (5.484,6.552) -- (5.43,6.659) -- (5.345,6.744) -- (5.237,6.799) -- (5.119,6.818) -- (5.119,6.818) -- (5.0,6.799) -- (4.893,6.744) -- (4.807,6.659) -- (4.753,6.552) -- (4.734,6.433) -- (4.753,6.314) -- (4.807,6.207) -- (4.893,6.122) -- (5.0,6.067) -- (5.119,6.049) -- cycle;
\node at (5.119,6.433) {\scalebox{1.604}{\small 5}};
\filldraw[fill=white, draw=black, line width=0.5pt] (9.813,8.4) -- (9.932,8.419) -- (10.039,8.473) -- (10.124,8.558) -- (10.179,8.666) -- (10.198,8.784) -- (10.179,8.903) -- (10.124,9.01) -- (10.039,9.096) -- (9.932,9.15) -- (9.813,9.169) -- (9.813,9.169) -- (9.694,9.15) -- (9.587,9.096) -- (9.502,9.01) -- (9.448,8.903) -- (9.429,8.784) -- (9.448,8.666) -- (9.502,8.558) -- (9.587,8.473) -- (9.694,8.419) -- (9.813,8.4) -- cycle;
\node at (9.813,8.784) {\scalebox{1.604}{\small 6}};
\filldraw[fill=white, draw=black, line width=0.5pt] (8.261,5.94) -- (8.38,5.959) -- (8.487,6.013) -- (8.572,6.098) -- (8.627,6.206) -- (8.646,6.324) -- (8.627,6.443) -- (8.572,6.55) -- (8.487,6.635) -- (8.38,6.69) -- (8.261,6.709) -- (8.261,6.709) -- (8.143,6.69) -- (8.035,6.635) -- (7.95,6.55) -- (7.896,6.443) -- (7.877,6.324) -- (7.896,6.206) -- (7.95,6.098) -- (8.035,6.013) -- (8.143,5.959) -- (8.261,5.94) -- cycle;
\node at (8.261,6.324) {\scalebox{1.604}{\small 7}};
\filldraw[fill=white, draw=black, line width=0.5pt] (3.253,5.13) -- (3.372,5.149) -- (3.479,5.204) -- (3.564,5.289) -- (3.619,5.396) -- (3.638,5.515) -- (3.619,5.634) -- (3.564,5.741) -- (3.479,5.826) -- (3.372,5.881) -- (3.253,5.899) -- (3.253,5.899) -- (3.134,5.881) -- (3.027,5.826) -- (2.942,5.741) -- (2.887,5.634) -- (2.869,5.515) -- (2.887,5.396) -- (2.942,5.289) -- (3.027,5.204) -- (3.134,5.149) -- (3.253,5.13) -- cycle;
\node at (3.253,5.515) {\scalebox{1.604}{\small 8}};
\filldraw[fill=white, draw=black, line width=0.5pt] (2.042,3.388) -- (2.16,3.406) -- (2.268,3.461) -- (2.353,3.546) -- (2.407,3.653) -- (2.426,3.772) -- (2.407,3.891) -- (2.353,3.998) -- (2.268,4.083) -- (2.16,4.138) -- (2.042,4.157) -- (2.042,4.157) -- (1.923,4.138) -- (1.816,4.083) -- (1.731,3.998) -- (1.676,3.891) -- (1.657,3.772) -- (1.676,3.653) -- (1.731,3.546) -- (1.816,3.461) -- (1.923,3.406) -- (2.042,3.388) -- cycle;
\node at (2.042,3.772) {\scalebox{1.604}{\small 9}};
\filldraw[fill=white, draw=black, line width=0.5pt] (11.457,3.523) -- (11.576,3.542) -- (11.683,3.596) -- (11.768,3.681) -- (11.823,3.789) -- (11.841,3.907) -- (11.823,4.026) -- (11.768,4.133) -- (11.683,4.219) -- (11.576,4.273) -- (11.457,4.292) -- (11.095,4.292) -- (10.976,4.273) -- (10.869,4.219) -- (10.784,4.133) -- (10.729,4.026) -- (10.71,3.907) -- (10.729,3.789) -- (10.784,3.681) -- (10.869,3.596) -- (10.976,3.542) -- (11.095,3.523) -- cycle;
\node at (11.276,3.907) {\scalebox{1.604}{\small 10}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.281,4.596) -- (6.4,4.615) -- (6.507,4.67) -- (6.592,4.755) -- (6.646,4.862) -- (6.665,4.981) -- (6.646,5.1) -- (6.592,5.207) -- (6.507,5.292) -- (6.4,5.347) -- (6.281,5.365) -- (5.919,5.365) -- (5.8,5.347) -- (5.693,5.292) -- (5.608,5.207) -- (5.553,5.1) -- (5.534,4.981) -- (5.553,4.862) -- (5.608,4.755) -- (5.693,4.67) -- (5.8,4.615) -- (5.919,4.596) -- cycle;
\node at (6.1,4.981) {\scalebox{1.604}{\small 11}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.212,2.739) -- (5.331,2.758) -- (5.438,2.813) -- (5.523,2.898) -- (5.578,3.005) -- (5.596,3.124) -- (5.578,3.243) -- (5.523,3.35) -- (5.438,3.435) -- (5.331,3.49) -- (5.212,3.508) -- (4.85,3.508) -- (4.731,3.49) -- (4.624,3.435) -- (4.539,3.35) -- (4.484,3.243) -- (4.466,3.124) -- (4.484,3.005) -- (4.539,2.898) -- (4.624,2.813) -- (4.731,2.758) -- (4.85,2.739) -- cycle;
\node at (5.031,3.124) {\scalebox{1.604}{\small 12}};
\filldraw[fill=white, draw=black, line width=0.5pt] (9.239,4.807) -- (9.358,4.825) -- (9.465,4.88) -- (9.55,4.965) -- (9.604,5.072) -- (9.623,5.191) -- (9.604,5.31) -- (9.55,5.417) -- (9.465,5.502) -- (9.358,5.557) -- (9.239,5.576) -- (8.877,5.576) -- (8.758,5.557) -- (8.651,5.502) -- (8.566,5.417) -- (8.511,5.31) -- (8.492,5.191) -- (8.511,5.072) -- (8.566,4.965) -- (8.651,4.88) -- (8.758,4.825) -- (8.877,4.807) -- cycle;
\node at (9.058,5.191) {\scalebox{1.604}{\small 13}};
\filldraw[fill=white, draw=black, line width=0.5pt] (8.565,2.994) -- (8.684,3.012) -- (8.791,3.067) -- (8.876,3.152) -- (8.931,3.259) -- (8.95,3.378) -- (8.931,3.497) -- (8.876,3.604) -- (8.791,3.689) -- (8.684,3.744) -- (8.565,3.763) -- (8.203,3.763) -- (8.084,3.744) -- (7.977,3.689) -- (7.892,3.604) -- (7.837,3.497) -- (7.819,3.378) -- (7.837,3.259) -- (7.892,3.152) -- (7.977,3.067) -- (8.084,3.012) -- (8.203,2.994) -- cycle;
\node at (8.384,3.378) {\scalebox{1.604}{\small 14}};
\filldraw[fill=white, draw=black, line width=0.5pt] (3.374,1.772) -- (3.493,1.791) -- (3.6,1.845) -- (3.685,1.93) -- (3.74,2.038) -- (3.759,2.156) -- (3.74,2.275) -- (3.685,2.382) -- (3.6,2.467) -- (3.493,2.522) -- (3.374,2.541) -- (3.012,2.541) -- (2.894,2.522) -- (2.786,2.467) -- (2.701,2.382) -- (2.647,2.275) -- (2.628,2.156) -- (2.647,2.038) -- (2.701,1.93) -- (2.786,1.845) -- (2.894,1.791) -- (3.012,1.772) -- cycle;
\node at (3.193,2.156) {\scalebox{1.604}{\small 15}};
\filldraw[fill=white, draw=black, line width=0.5pt] (9.647,2.287) -- (9.765,2.306) -- (9.873,2.361) -- (9.958,2.446) -- (10.012,2.553) -- (10.031,2.672) -- (10.012,2.79) -- (9.958,2.898) -- (9.873,2.983) -- (9.765,3.037) -- (9.647,3.056) -- (9.285,3.056) -- (9.166,3.037) -- (9.059,2.983) -- (8.974,2.898) -- (8.919,2.79) -- (8.9,2.672) -- (8.919,2.553) -- (8.974,2.446) -- (9.059,2.361) -- (9.166,2.306) -- (9.285,2.287) -- cycle;
\node at (9.466,2.672) {\scalebox{1.604}{\small 16}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.476,1.539) -- (6.595,1.558) -- (6.702,1.612) -- (6.787,1.697) -- (6.841,1.805) -- (6.86,1.923) -- (6.841,2.042) -- (6.787,2.149) -- (6.702,2.235) -- (6.595,2.289) -- (6.476,2.308) -- (6.114,2.308) -- (5.995,2.289) -- (5.888,2.235) -- (5.803,2.149) -- (5.748,2.042) -- (5.729,1.923) -- (5.748,1.805) -- (5.803,1.697) -- (5.888,1.612) -- (5.995,1.558) -- (6.114,1.539) -- cycle;
\node at (6.295,1.923) {\scalebox{1.604}{\small 17}};
\filldraw[fill=yellow!35, draw=black, line width=0.5pt] (7.898,1.593) -- (8.498,1.593) -- (8.498,2.193) -- (7.898,2.193) -- cycle;
\node at (8.198,1.893) {\scalebox{1.604}{\small a}};
\filldraw[fill=green!18, draw=black, line width=0.5pt] (2.057,8.953) -- (2.657,8.953) -- (2.657,9.553) -- (2.057,9.553) -- cycle;
\node at (2.357,9.253) {\scalebox{1.604}{\small b}};
\filldraw[fill=red!16, draw=black, line width=0.5pt] (12.169,3.88) -- (12.769,3.88) -- (12.769,4.48) -- (12.169,4.48) -- cycle;
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\end{center}
\noindent{\small\itshape Deux carrefours reliés par une rue n'ont jamais la même couleur.}\par\addvspace{0.4em}
\noindent \textbf{1.} Le coloriage est \textbf{forcé} : une fois la couleur d'un carrefour choisie, celle de tous les autres suit, de proche en proche.\par\addvspace{0.35em}
\begin{center}
\renewcommand{\arraystretch}{1.35}
\begin{tabular}{|c|c|c|}
\hline
\cellcolor{blue!7}\bfseries Couleur & \cellcolor{blue!7}\bfseries Carrefours & \cellcolor{blue!7}\bfseries Nombre \\ \hline
sombres & A, D, F, G, J, K & 6 \\ \hline
clairs & B, C, E, H, I, 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 Four ⑭} vers le nord jusqu'à Carrefour de l'Hôpital \textbf{(H)}.\par\addvspace{0.35em}
\noindent Il tourne à gauche dans le \textbf{sentier des Prés ⑪}, vers l'ouest, jusqu'à Carrefour du Lavoir \textbf{(G)}.\par\addvspace{0.35em}
\noindent Il tourne à gauche dans le \textbf{chemin du Lavoir ⑫}, vers le sud, jusqu'à Rond-point de la Gare \textbf{(L)}.\par\addvspace{0.35em}
\noindent Il tourne à droite dans la \textbf{rue des Écoles ⑮}, vers l'ouest, jusqu'à Coin du Lavoir \textbf{(J)}.\par\addvspace{0.35em}
\noindent Il tourne à droite dans le \textbf{chemin de Ronde ⑨}, vers le nord, jusqu'à Carrefour du Moulin \textbf{(E)}.\par\addvspace{0.35em}
\noindent Il continue tout droit dans l'\textbf{allée des Peupliers ②}, vers le nord, jusqu'à Place des Tanneurs \textbf{(A)}.\par\addvspace{0.35em}
\noindent Il tourne à droite dans la \textbf{rue Haute ①}, vers l'est, jusqu'à Carrefour de la Mairie \textbf{(C)}.\par\addvspace{0.35em}
\noindent Il continue tout droit dans le \textbf{chemin des Vignes ④}, vers l'est, jusqu'à Rond-point du Pont \textbf{(D)}.\par\addvspace{0.35em}
\noindent Il continue tout droit dans la \textbf{rue Basse ⑥}, vers l'est, jusqu'à Placette des Ormes \textbf{(B)}.\par\addvspace{0.35em}
\noindent Il tourne à droite dans la \textbf{rue du Stade ③}, vers le sud, jusqu'à Rond-point du Stade \textbf{(F)}.\par\addvspace{0.35em}
\noindent Il continue tout droit dans la \textbf{rue Neuve ⑩}, vers le sud, jusqu'à Place du Marché \textbf{(I)}.\par\addvspace{0.35em}
\noindent Il tourne à droite dans le \textbf{quai aux Fleurs ⑯}, vers l'ouest, jusqu'à Rond-point de la Poste \textbf{(K)}.\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}
