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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 D, et doit s'arrêter à chaque carrefour exactement une fois.} Il emprunte les rues qu'il veut et n'a pas à toutes les parcourir.\par\addvspace{0.35em}
\begin{center}
\renewcommand{\arraystretch}{1.35}
\begin{tabular}{|c|c|c|c|}
\hline
\cellcolor{black!32}\bfseries Les rues & ⑨ rue de la Mairie & \cellcolor{black!32}\bfseries Les carrefours & Ⓘ Carrefour de la Mairie \\ \hline
① rue du Moulin & ⑩ passage du Marché & Ⓐ Carrefour de l'Hôpital & Ⓙ Placette des Ormes \\ \hline
② boulevard du Parc & ⑪ quai aux Fleurs & Ⓑ Fontaine Notre-Dame & Ⓚ Place Sainte-Croix \\ \hline
③ chemin du Lavoir & ⑫ venelle du Chat & Ⓒ Place du Marché & Ⓛ Carrefour du Moulin \\ \hline
④ rue Basse & ⑬ chemin des Vignes & Ⓓ Rond-point du Pont & \cellcolor{black!32}\bfseries Les bâtiments \\ \hline
⑤ sentier des Prés & ⑭ rue du Puits & Ⓔ Rond-point des Vaches & \textbf{a} l'école \\ \hline
⑥ rue des Jardins & ⑮ rue du Four & Ⓕ Rond-point du Stade & \textbf{b} la boulangerie \\ \hline
⑦ rue Verte & ⑯ allée des Tilleuls & Ⓖ Rond-point de la Poste & \textbf{c} le stade \\ \hline
⑧ allée des Peupliers & ⑰ rue des Écoles & Ⓗ Rond-point de la Gare & \textbf{d} le lavoir \\ \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] (1.302,4.402) -- (1.557,4.493) -- (1.814,4.578) -- (2.073,4.658) -- (2.333,4.731) -- (2.596,4.798) -- (2.86,4.859) -- (3.125,4.913) -- (3.392,4.962) -- (3.659,5.004) -- (3.928,5.04) -- (4.197,5.069) -- (4.467,5.092) -- (4.737,5.109) -- (5.007,5.119);
\draw[line width=0.5pt] (1.302,4.402) -- (1.34,4.215) -- (1.381,4.03) -- (1.427,3.845) -- (1.477,3.662) -- (1.532,3.479) -- (1.591,3.298) -- (1.654,3.119) -- (1.721,2.941) -- (1.793,2.764) -- (1.869,2.59) -- (1.948,2.417) -- (2.032,2.246) -- (2.12,2.077) -- (2.211,1.911);
\draw[line width=0.5pt] (2.211,1.911) -- (2.41,1.917) -- (2.61,1.918) -- (2.809,1.915) -- (3.008,1.906) -- (3.207,1.894) -- (3.406,1.876) -- (3.604,1.854) -- (3.801,1.827) -- (3.998,1.796) -- (4.194,1.76) -- (4.39,1.719) -- (4.584,1.674) -- (4.777,1.624) -- (4.968,1.57);
\draw[line width=0.5pt] (4.968,1.57) -- (5.22,1.549) -- (5.473,1.534) -- (5.726,1.525) -- (5.979,1.522) -- (6.233,1.525) -- (6.486,1.534) -- (6.739,1.549) -- (6.991,1.57) -- (7.243,1.597) -- (7.495,1.63) -- (7.745,1.668) -- (7.994,1.713) -- (8.242,1.763) -- (8.489,1.819);
\filldraw[fill=white, draw=black, line width=0.5pt] (5.818,11.57) -- (5.79,11.713) -- (5.709,11.834) -- (5.588,11.915) -- (5.445,11.943) -- (5.302,11.915) -- (5.181,11.834) -- (5.1,11.713) -- (5.072,11.57) -- (5.1,11.427) -- (5.181,11.306) -- (5.302,11.225) -- (5.445,11.197) -- (5.588,11.225) -- (5.709,11.306) -- (5.79,11.427) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (1.668,11.379) -- (1.639,11.522) -- (1.558,11.643) -- (1.437,11.724) -- (1.294,11.752) -- (1.152,11.724) -- (1.031,11.643) -- (0.95,11.522) -- (0.921,11.379) -- (0.95,11.236) -- (1.031,11.115) -- (1.152,11.034) -- (1.294,11.006) -- (1.437,11.034) -- (1.558,11.115) -- (1.639,11.236) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (8.108,11.037) -- (8.079,11.179) -- (7.998,11.3) -- (7.877,11.381) -- (7.734,11.41) -- (7.592,11.381) -- (7.471,11.3) -- (7.39,11.179) -- (7.361,11.037) -- (7.39,10.894) -- (7.471,10.773) -- (7.592,10.692) -- (7.734,10.663) -- (7.877,10.692) -- (7.998,10.773) -- (8.079,10.894) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (2.014,8.304) -- (1.985,8.447) -- (1.904,8.568) -- (1.783,8.649) -- (1.64,8.677) -- (1.497,8.649) -- (1.376,8.568) -- (1.296,8.447) -- (1.267,8.304) -- (1.296,8.161) -- (1.376,8.04) -- (1.497,7.959) -- (1.64,7.931) -- (1.783,7.959) -- (1.904,8.04) -- (1.985,8.161) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (5.055,8.14) -- (5.026,8.283) -- (4.945,8.404) -- (4.824,8.485) -- (4.682,8.513) -- (4.539,8.485) -- (4.418,8.404) -- (4.337,8.283) -- (4.308,8.14) -- (4.337,7.997) -- (4.418,7.876) -- (4.539,7.795) -- (4.682,7.766) -- (4.824,7.795) -- (4.945,7.876) -- (5.026,7.997) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (8.923,8.001) -- (8.895,8.144) -- (8.814,8.265) -- (8.693,8.346) -- (8.55,8.374) -- (8.407,8.346) -- (8.286,8.265) -- (8.205,8.144) -- (8.177,8.001) -- (8.205,7.858) -- (8.286,7.737) -- (8.407,7.656) -- (8.55,7.628) -- (8.693,7.656) -- (8.814,7.737) -- (8.895,7.858) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (5.38,5.119) -- (5.352,5.262) -- (5.271,5.383) -- (5.15,5.464) -- (5.007,5.493) -- (4.864,5.464) -- (4.743,5.383) -- (4.662,5.262) -- (4.634,5.119) -- (4.662,4.976) -- (4.743,4.855) -- (4.864,4.774) -- (5.007,4.746) -- (5.15,4.774) -- (5.271,4.855) -- (5.352,4.976) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (8.541,4.815) -- (8.512,4.958) -- (8.431,5.079) -- (8.31,5.16) -- (8.168,5.188) -- (8.025,5.16) -- (7.904,5.079) -- (7.823,4.958) -- (7.794,4.815) -- (7.823,4.672) -- (7.904,4.551) -- (8.025,4.47) -- (8.168,4.442) -- (8.31,4.47) -- (8.431,4.551) -- (8.512,4.672) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (1.676,4.402) -- (1.647,4.545) -- (1.566,4.666) -- (1.445,4.747) -- (1.302,4.775) -- (1.16,4.747) -- (1.038,4.666) -- (0.958,4.545) -- (0.929,4.402) -- (0.958,4.259) -- (1.038,4.138) -- (1.16,4.057) -- (1.302,4.029) -- (1.445,4.057) -- (1.566,4.138) -- (1.647,4.259) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (2.585,1.911) -- (2.556,2.053) -- (2.475,2.175) -- (2.354,2.255) -- (2.211,2.284) -- (2.069,2.255) -- (1.947,2.175) -- (1.867,2.053) -- (1.838,1.911) -- (1.867,1.768) -- (1.947,1.647) -- (2.069,1.566) -- (2.211,1.537) -- (2.354,1.566) -- (2.475,1.647) -- (2.556,1.768) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (8.862,1.819) -- (8.834,1.962) -- (8.753,2.083) -- (8.632,2.164) -- (8.489,2.192) -- (8.346,2.164) -- (8.225,2.083) -- (8.144,1.962) -- (8.116,1.819) -- (8.144,1.676) -- (8.225,1.555) -- (8.346,1.474) -- (8.489,1.446) -- (8.632,1.474) -- (8.753,1.555) -- (8.834,1.676) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (5.341,1.57) -- (5.313,1.713) -- (5.232,1.834) -- (5.111,1.915) -- (4.968,1.943) -- (4.825,1.915) -- (4.704,1.834) -- (4.623,1.713) -- (4.595,1.57) -- (4.623,1.427) -- (4.704,1.306) -- (4.825,1.225) -- (4.968,1.197) -- (5.111,1.225) -- (5.232,1.306) -- (5.313,1.427) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (6.655,11.199) -- (6.774,11.218) -- (6.881,11.272) -- (6.966,11.357) -- (7.021,11.465) -- (7.04,11.583) -- (7.021,11.702) -- (6.966,11.809) -- (6.881,11.894) -- (6.774,11.949) -- (6.655,11.968) -- (6.655,11.968) -- (6.536,11.949) -- (6.429,11.894) -- (6.344,11.809) -- (6.289,11.702) -- (6.271,11.583) -- (6.289,11.465) -- (6.344,11.357) -- (6.429,11.272) -- (6.536,11.218) -- (6.655,11.199) -- cycle;
\node at (6.655,11.583) {\scalebox{1.28}{\small 1}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.58,9.355) -- (5.699,9.374) -- (5.806,9.429) -- (5.891,9.514) -- (5.946,9.621) -- (5.965,9.74) -- (5.946,9.859) -- (5.891,9.966) -- (5.806,10.051) -- (5.699,10.105) -- (5.58,10.124) -- (5.58,10.124) -- (5.461,10.105) -- (5.354,10.051) -- (5.269,9.966) -- (5.215,9.859) -- (5.196,9.74) -- (5.215,9.621) -- (5.269,9.514) -- (5.354,9.429) -- (5.461,9.374) -- (5.58,9.355) -- cycle;
\node at (5.58,9.74) {\scalebox{1.28}{\small 2}};
\filldraw[fill=white, draw=black, line width=0.5pt] (3.36,11.303) -- (3.479,11.322) -- (3.586,11.376) -- (3.671,11.461) -- (3.726,11.568) -- (3.745,11.687) -- (3.726,11.806) -- (3.671,11.913) -- (3.586,11.998) -- (3.479,12.053) -- (3.36,12.072) -- (3.36,12.072) -- (3.241,12.053) -- (3.134,11.998) -- (3.049,11.913) -- (2.994,11.806) -- (2.976,11.687) -- (2.994,11.568) -- (3.049,11.461) -- (3.134,11.376) -- (3.241,11.322) -- (3.36,11.303) -- cycle;
\node at (3.36,11.687) {\scalebox{1.28}{\small 3}};
\filldraw[fill=white, draw=black, line width=0.5pt] (1.976,9.514) -- (2.095,9.533) -- (2.202,9.588) -- (2.287,9.673) -- (2.342,9.78) -- (2.361,9.899) -- (2.342,10.017) -- (2.287,10.125) -- (2.202,10.21) -- (2.095,10.264) -- (1.976,10.283) -- (1.976,10.283) -- (1.858,10.264) -- (1.75,10.21) -- (1.665,10.125) -- (1.611,10.017) -- (1.592,9.899) -- (1.611,9.78) -- (1.665,9.673) -- (1.75,9.588) -- (1.858,9.533) -- (1.976,9.514) -- cycle;
\node at (1.976,9.899) {\scalebox{1.28}{\small 4}};
\filldraw[fill=white, draw=black, line width=0.5pt] (8.388,9.201) -- (8.507,9.219) -- (8.614,9.274) -- (8.699,9.359) -- (8.754,9.466) -- (8.773,9.585) -- (8.754,9.704) -- (8.699,9.811) -- (8.614,9.896) -- (8.507,9.951) -- (8.388,9.97) -- (8.388,9.97) -- (8.27,9.951) -- (8.162,9.896) -- (8.077,9.811) -- (8.023,9.704) -- (8.004,9.585) -- (8.023,9.466) -- (8.077,9.359) -- (8.162,9.274) -- (8.27,9.219) -- (8.388,9.201) -- cycle;
\node at (8.388,9.585) {\scalebox{1.28}{\small 5}};
\filldraw[fill=white, draw=black, line width=0.5pt] (3.188,8.347) -- (3.307,8.366) -- (3.414,8.42) -- (3.5,8.505) -- (3.554,8.612) -- (3.573,8.731) -- (3.554,8.85) -- (3.5,8.957) -- (3.414,9.042) -- (3.307,9.097) -- (3.188,9.116) -- (3.188,9.116) -- (3.07,9.097) -- (2.962,9.042) -- (2.877,8.957) -- (2.823,8.85) -- (2.804,8.731) -- (2.823,8.612) -- (2.877,8.505) -- (2.962,8.42) -- (3.07,8.366) -- (3.188,8.347) -- cycle;
\node at (3.188,8.731) {\scalebox{1.28}{\small 6}};
\filldraw[fill=white, draw=black, line width=0.5pt] (1.693,5.949) -- (1.812,5.968) -- (1.919,6.023) -- (2.005,6.108) -- (2.059,6.215) -- (2.078,6.334) -- (2.059,6.452) -- (2.005,6.56) -- (1.919,6.645) -- (1.812,6.699) -- (1.693,6.718) -- (1.693,6.718) -- (1.575,6.699) -- (1.467,6.645) -- (1.382,6.56) -- (1.328,6.452) -- (1.309,6.334) -- (1.328,6.215) -- (1.382,6.108) -- (1.467,6.023) -- (1.575,5.968) -- (1.693,5.949) -- cycle;
\node at (1.693,6.334) {\scalebox{1.28}{\small 7}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.635,8.23) -- (6.754,8.249) -- (6.861,8.303) -- (6.946,8.388) -- (7.001,8.496) -- (7.02,8.614) -- (7.001,8.733) -- (6.946,8.84) -- (6.861,8.925) -- (6.754,8.98) -- (6.635,8.999) -- (6.635,8.999) -- (6.516,8.98) -- (6.409,8.925) -- (6.324,8.84) -- (6.27,8.733) -- (6.251,8.614) -- (6.27,8.496) -- (6.324,8.388) -- (6.409,8.303) -- (6.516,8.249) -- (6.635,8.23) -- cycle;
\node at (6.635,8.614) {\scalebox{1.28}{\small 8}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.102,6.273) -- (5.221,6.292) -- (5.328,6.346) -- (5.413,6.431) -- (5.468,6.538) -- (5.487,6.657) -- (5.468,6.776) -- (5.413,6.883) -- (5.328,6.968) -- (5.221,7.023) -- (5.102,7.042) -- (5.102,7.042) -- (4.983,7.023) -- (4.876,6.968) -- (4.791,6.883) -- (4.736,6.776) -- (4.718,6.657) -- (4.736,6.538) -- (4.791,6.431) -- (4.876,6.346) -- (4.983,6.292) -- (5.102,6.273) -- cycle;
\node at (5.102,6.657) {\scalebox{1.28}{\small 9}};
\filldraw[fill=white, draw=black, line width=0.5pt] (9.053,5.962) -- (9.172,5.981) -- (9.279,6.035) -- (9.364,6.12) -- (9.419,6.228) -- (9.438,6.346) -- (9.419,6.465) -- (9.364,6.572) -- (9.279,6.658) -- (9.172,6.712) -- (9.053,6.731) -- (8.691,6.731) -- (8.572,6.712) -- (8.465,6.658) -- (8.38,6.572) -- (8.325,6.465) -- (8.307,6.346) -- (8.325,6.228) -- (8.38,6.12) -- (8.465,6.035) -- (8.572,5.981) -- (8.691,5.962) -- cycle;
\node at (8.872,6.346) {\scalebox{1.28}{\small 10}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.793,4.835) -- (6.911,4.854) -- (7.019,4.908) -- (7.104,4.993) -- (7.158,5.101) -- (7.177,5.219) -- (7.158,5.338) -- (7.104,5.445) -- (7.019,5.531) -- (6.911,5.585) -- (6.793,5.604) -- (6.431,5.604) -- (6.312,5.585) -- (6.205,5.531) -- (6.12,5.445) -- (6.065,5.338) -- (6.046,5.219) -- (6.065,5.101) -- (6.12,4.993) -- (6.205,4.908) -- (6.312,4.854) -- (6.431,4.835) -- cycle;
\node at (6.612,5.219) {\scalebox{1.28}{\small 11}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.7,2.954) -- (5.818,2.973) -- (5.926,3.028) -- (6.011,3.113) -- (6.065,3.22) -- (6.084,3.339) -- (6.065,3.458) -- (6.011,3.565) -- (5.926,3.65) -- (5.818,3.705) -- (5.7,3.723) -- (5.338,3.723) -- (5.219,3.705) -- (5.112,3.65) -- (5.027,3.565) -- (4.972,3.458) -- (4.953,3.339) -- (4.972,3.22) -- (5.027,3.113) -- (5.112,3.028) -- (5.219,2.973) -- (5.338,2.954) -- cycle;
\node at (5.519,3.339) {\scalebox{1.28}{\small 12}};
\filldraw[fill=white, draw=black, line width=0.5pt] (8.768,2.96) -- (8.887,2.979) -- (8.994,3.034) -- (9.079,3.119) -- (9.134,3.226) -- (9.152,3.345) -- (9.134,3.464) -- (9.079,3.571) -- (8.994,3.656) -- (8.887,3.71) -- (8.768,3.729) -- (8.406,3.729) -- (8.287,3.71) -- (8.18,3.656) -- (8.095,3.571) -- (8.04,3.464) -- (8.022,3.345) -- (8.04,3.226) -- (8.095,3.119) -- (8.18,3.034) -- (8.287,2.979) -- (8.406,2.96) -- cycle;
\node at (8.587,3.345) {\scalebox{1.28}{\small 13}};
\filldraw[fill=white, draw=black, line width=0.5pt] (3.233,4.906) -- (3.352,4.925) -- (3.459,4.98) -- (3.544,5.065) -- (3.599,5.172) -- (3.618,5.291) -- (3.599,5.41) -- (3.544,5.517) -- (3.459,5.602) -- (3.352,5.657) -- (3.233,5.675) -- (2.871,5.675) -- (2.752,5.657) -- (2.645,5.602) -- (2.56,5.517) -- (2.505,5.41) -- (2.487,5.291) -- (2.505,5.172) -- (2.56,5.065) -- (2.645,4.98) -- (2.752,4.925) -- (2.871,4.906) -- cycle;
\node at (3.052,5.291) {\scalebox{1.28}{\small 14}};
\filldraw[fill=white, draw=black, line width=0.5pt] (2.196,2.866) -- (2.315,2.885) -- (2.422,2.939) -- (2.507,3.024) -- (2.562,3.132) -- (2.581,3.25) -- (2.562,3.369) -- (2.507,3.477) -- (2.422,3.562) -- (2.315,3.616) -- (2.196,3.635) -- (1.834,3.635) -- (1.716,3.616) -- (1.608,3.562) -- (1.523,3.477) -- (1.469,3.369) -- (1.45,3.25) -- (1.469,3.132) -- (1.523,3.024) -- (1.608,2.939) -- (1.716,2.885) -- (1.834,2.866) -- cycle;
\node at (2.015,3.25) {\scalebox{1.28}{\small 15}};
\filldraw[fill=white, draw=black, line width=0.5pt] (3.832,1.851) -- (3.951,1.87) -- (4.058,1.925) -- (4.143,2.01) -- (4.198,2.117) -- (4.217,2.236) -- (4.198,2.354) -- (4.143,2.462) -- (4.058,2.547) -- (3.951,2.601) -- (3.832,2.62) -- (3.47,2.62) -- (3.351,2.601) -- (3.244,2.547) -- (3.159,2.462) -- (3.104,2.354) -- (3.086,2.236) -- (3.104,2.117) -- (3.159,2.01) -- (3.244,1.925) -- (3.351,1.87) -- (3.47,1.851) -- cycle;
\node at (3.651,2.236) {\scalebox{1.28}{\small 16}};
\filldraw[fill=white, draw=black, line width=0.5pt] (7.379,1.594) -- (7.498,1.613) -- (7.605,1.668) -- (7.69,1.753) -- (7.745,1.86) -- (7.764,1.979) -- (7.745,2.098) -- (7.69,2.205) -- (7.605,2.29) -- (7.498,2.344) -- (7.379,2.363) -- (7.017,2.363) -- (6.898,2.344) -- (6.791,2.29) -- (6.706,2.205) -- (6.652,2.098) -- (6.633,1.979) -- (6.652,1.86) -- (6.706,1.753) -- (6.791,1.668) -- (6.898,1.613) -- (7.017,1.594) -- cycle;
\node at (7.198,1.979) {\scalebox{1.28}{\small 17}};
\filldraw[fill=yellow!35, draw=black, line width=0.5pt] (1.34,8.004) -- (1.94,8.004) -- (1.94,8.604) -- (1.34,8.604) -- cycle;
\node at (1.64,8.304) {\scalebox{1.28}{\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 & B, C, E, H, I, L & 6 \\ \hline
clairs & A, D, F, G, J, K & 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 Basse ④} vers le nord jusqu'à Fontaine Notre-Dame \textbf{(B)}.\par\addvspace{0.35em}
\noindent Il tourne à droite dans le \textbf{chemin du Lavoir ③}, vers l'est, jusqu'à Carrefour de l'Hôpital \textbf{(A)}.\par\addvspace{0.35em}
\noindent Il continue tout droit dans la \textbf{rue du Moulin ①}, vers l'est, jusqu'à Place du Marché \textbf{(C)}.\par\addvspace{0.35em}
\noindent Il tourne à droite dans le \textbf{sentier des Prés ⑤}, vers le sud, jusqu'à Rond-point du Stade \textbf{(F)}.\par\addvspace{0.35em}
\noindent Il tourne à droite dans l'\textbf{allée des Peupliers ⑧}, vers l'ouest, jusqu'à Rond-point des Vaches \textbf{(E)}.\par\addvspace{0.35em}
\noindent Il tourne à gauche dans la \textbf{rue de la Mairie ⑨}, vers le sud, jusqu'à Rond-point de la Poste \textbf{(G)}.\par\addvspace{0.35em}
\noindent Il tourne à gauche dans le \textbf{quai aux Fleurs ⑪}, vers l'est, jusqu'à Rond-point de la Gare \textbf{(H)}.\par\addvspace{0.35em}
\noindent Il tourne à droite dans le \textbf{chemin des Vignes ⑬}, vers le sud, jusqu'à Place Sainte-Croix \textbf{(K)}.\par\addvspace{0.35em}
\noindent Il tourne à droite dans la \textbf{rue des Écoles ⑰}, vers l'ouest, jusqu'à Carrefour du Moulin \textbf{(L)}.\par\addvspace{0.35em}
\noindent Il continue tout droit dans l'\textbf{allée des Tilleuls ⑯}, vers l'ouest, jusqu'à Placette des Ormes \textbf{(J)}.\par\addvspace{0.35em}
\noindent Il tourne à droite dans la \textbf{rue du Four ⑮}, vers le nord, jusqu'à Carrefour de la Mairie \textbf{(I)}.\par\addvspace{0.35em}
\noindent Il continue tout droit dans la \textbf{rue Verte ⑦}, vers le nord, jusqu'à Rond-point du Pont \textbf{(D)}.\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}
