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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 F, 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 rue Haute & Ⓑ Rond-point du Pont & Ⓛ Placette des Ormes \\ \hline
① impasse Sainte-Anne & ⑪ rue du Stade & Ⓒ Place de l'Église & Ⓜ Coin du Lavoir \\ \hline
② passage du Marché & ⑫ avenue de la Gare & Ⓓ Rond-point du Stade & \cellcolor{black!32}\bfseries Les bâtiments \\ \hline
③ rue de l'Église & ⑬ rue Verte & Ⓔ Carrefour de l'Hôpital & \textbf{a} l'école \\ \hline
④ rue Basse & ⑭ chemin Creux & Ⓕ Rond-point des Vaches & \textbf{b} l'église \\ \hline
⑤ chemin du Lavoir & ⑮ venelle du Chat & Ⓖ Place du Marché & \textbf{c} la mairie \\ \hline
⑥ allée des Peupliers & ⑯ rue des Écoles & Ⓗ Place des Tanneurs & \textbf{d} la gendarmerie \\ \hline
⑦ rue Neuve & ⑰ allée des Tilleuls & Ⓘ Carrefour des Tilleuls &  \\ \hline
⑧ rue Pasteur & \cellcolor{black!32}\bfseries Les carrefours & Ⓙ Place aux Herbes &  \\ \hline
⑨ rue des Jardins & Ⓐ Fontaine Notre-Dame & Ⓚ Carrefour de la Mairie &  \\ \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] (1.61,6.367) -- (1.783,6.422) -- (1.957,6.474) -- (2.133,6.521) -- (2.309,6.564) -- (2.486,6.603) -- (2.665,6.638) -- (2.844,6.668) -- (3.023,6.695) -- (3.204,6.717) -- (3.384,6.735) -- (3.566,6.749) -- (3.747,6.758) -- (3.928,6.763) -- (4.11,6.764);
\draw[line width=0.5pt] (8.331,4.539) -- (8.324,4.318) -- (8.322,4.096) -- (8.325,3.874) -- (8.334,3.652) -- (8.348,3.43) -- (8.367,3.209) -- (8.391,2.988) -- (8.42,2.768) -- (8.455,2.548) -- (8.494,2.33) -- (8.539,2.112) -- (8.589,1.896) -- (8.644,1.681) -- (8.704,1.467);
\draw[line width=0.5pt] (4.008,4.065) -- (4.163,4.075) -- (4.318,4.081) -- (4.473,4.084) -- (4.629,4.083) -- (4.784,4.078) -- (4.939,4.07) -- (5.094,4.058) -- (5.248,4.043) -- (5.402,4.024) -- (5.556,4.001) -- (5.709,3.975) -- (5.861,3.945) -- (6.013,3.911) -- (6.163,3.874);
\draw[line width=0.5pt] (6.163,3.874) -- (6.324,3.897) -- (6.484,3.925) -- (6.644,3.956) -- (6.803,3.991) -- (6.961,4.029) -- (7.118,4.071) -- (7.275,4.117) -- (7.43,4.167) -- (7.583,4.22) -- (7.736,4.277) -- (7.887,4.337) -- (8.037,4.401) -- (8.185,4.469) -- (8.331,4.539);
\draw[line width=0.5pt] (6.163,3.874) -- (6.192,3.73) -- (6.217,3.586) -- (6.239,3.44) -- (6.257,3.295) -- (6.272,3.149) -- (6.284,3.002) -- (6.292,2.855) -- (6.296,2.709) -- (6.297,2.562) -- (6.295,2.415) -- (6.289,2.268) -- (6.28,2.122) -- (6.267,1.975) -- (6.251,1.83);
\draw[line width=0.5pt] (6.251,1.83) -- (6.421,1.777) -- (6.592,1.729) -- (6.764,1.684) -- (6.938,1.644) -- (7.112,1.607) -- (7.287,1.575) -- (7.463,1.547) -- (7.639,1.523) -- (7.816,1.503) -- (7.993,1.488) -- (8.171,1.476) -- (8.349,1.469) -- (8.526,1.466) -- (8.704,1.467);
\filldraw[fill=white, draw=black, line width=0.5pt] (6.898,11.467) -- (6.87,11.61) -- (6.789,11.731) -- (6.668,11.812) -- (6.525,11.84) -- (6.382,11.812) -- (6.261,11.731) -- (6.18,11.61) -- (6.151,11.467) -- (6.18,11.324) -- (6.261,11.203) -- (6.382,11.122) -- (6.525,11.094) -- (6.668,11.122) -- (6.789,11.203) -- (6.87,11.324) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (4.331,9.223) -- (4.303,9.366) -- (4.222,9.487) -- (4.101,9.568) -- (3.958,9.596) -- (3.815,9.568) -- (3.694,9.487) -- (3.613,9.366) -- (3.585,9.223) -- (3.613,9.08) -- (3.694,8.959) -- (3.815,8.878) -- (3.958,8.85) -- (4.101,8.878) -- (4.222,8.959) -- (4.303,9.08) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (1.711,8.833) -- (1.682,8.976) -- (1.601,9.097) -- (1.48,9.178) -- (1.338,9.206) -- (1.195,9.178) -- (1.074,9.097) -- (0.993,8.976) -- (0.964,8.833) -- (0.993,8.69) -- (1.074,8.569) -- (1.195,8.488) -- (1.338,8.46) -- (1.48,8.488) -- (1.601,8.569) -- (1.682,8.69) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (6.957,8.736) -- (6.929,8.879) -- (6.848,9.0) -- (6.727,9.081) -- (6.584,9.11) -- (6.441,9.081) -- (6.32,9.0) -- (6.239,8.879) -- (6.211,8.736) -- (6.239,8.594) -- (6.32,8.473) -- (6.441,8.392) -- (6.584,8.363) -- (6.727,8.392) -- (6.848,8.473) -- (6.929,8.594) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (6.271,6.832) -- (6.243,6.975) -- (6.162,7.096) -- (6.041,7.177) -- (5.898,7.206) -- (5.755,7.177) -- (5.634,7.096) -- (5.553,6.975) -- (5.525,6.832) -- (5.553,6.69) -- (5.634,6.568) -- (5.755,6.488) -- (5.898,6.459) -- (6.041,6.488) -- (6.162,6.568) -- (6.243,6.69) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (4.483,6.764) -- (4.455,6.907) -- (4.374,7.028) -- (4.253,7.109) -- (4.11,7.137) -- (3.967,7.109) -- (3.846,7.028) -- (3.765,6.907) -- (3.736,6.764) -- (3.765,6.621) -- (3.846,6.5) -- (3.967,6.419) -- (4.11,6.391) -- (4.253,6.419) -- (4.374,6.5) -- (4.455,6.621) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (9.339,6.569) -- (9.311,6.712) -- (9.23,6.833) -- (9.109,6.914) -- (8.966,6.942) -- (8.823,6.914) -- (8.702,6.833) -- (8.621,6.712) -- (8.593,6.569) -- (8.621,6.426) -- (8.702,6.305) -- (8.823,6.224) -- (8.966,6.196) -- (9.109,6.224) -- (9.23,6.305) -- (9.311,6.426) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (1.984,6.367) -- (1.955,6.509) -- (1.874,6.631) -- (1.753,6.711) -- (1.61,6.74) -- (1.468,6.711) -- (1.347,6.631) -- (1.266,6.509) -- (1.237,6.367) -- (1.266,6.224) -- (1.347,6.103) -- (1.468,6.022) -- (1.61,5.993) -- (1.753,6.022) -- (1.874,6.103) -- (1.955,6.224) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (8.704,4.539) -- (8.676,4.682) -- (8.595,4.803) -- (8.474,4.884) -- (8.331,4.913) -- (8.188,4.884) -- (8.067,4.803) -- (7.986,4.682) -- (7.958,4.539) -- (7.986,4.397) -- (8.067,4.275) -- (8.188,4.195) -- (8.331,4.166) -- (8.474,4.195) -- (8.595,4.275) -- (8.676,4.397) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (4.382,4.065) -- (4.353,4.208) -- (4.272,4.329) -- (4.151,4.41) -- (4.008,4.438) -- (3.866,4.41) -- (3.745,4.329) -- (3.664,4.208) -- (3.635,4.065) -- (3.664,3.922) -- (3.745,3.801) -- (3.866,3.72) -- (4.008,3.692) -- (4.151,3.72) -- (4.272,3.801) -- (4.353,3.922) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (6.536,3.874) -- (6.508,4.017) -- (6.427,4.138) -- (6.306,4.219) -- (6.163,4.247) -- (6.02,4.219) -- (5.899,4.138) -- (5.818,4.017) -- (5.79,3.874) -- (5.818,3.731) -- (5.899,3.61) -- (6.02,3.529) -- (6.163,3.501) -- (6.306,3.529) -- (6.427,3.61) -- (6.508,3.731) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (6.624,1.83) -- (6.596,1.972) -- (6.515,2.093) -- (6.394,2.174) -- (6.251,2.203) -- (6.108,2.174) -- (5.987,2.093) -- (5.906,1.972) -- (5.878,1.83) -- (5.906,1.687) -- (5.987,1.566) -- (6.108,1.485) -- (6.251,1.456) -- (6.394,1.485) -- (6.515,1.566) -- (6.596,1.687) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (9.077,1.467) -- (9.049,1.61) -- (8.968,1.731) -- (8.847,1.812) -- (8.704,1.84) -- (8.561,1.812) -- (8.44,1.731) -- (8.359,1.61) -- (8.331,1.467) -- (8.359,1.324) -- (8.44,1.203) -- (8.561,1.122) -- (8.704,1.094) -- (8.847,1.122) -- (8.968,1.203) -- (9.049,1.324) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (6.057,9.706) -- (6.176,9.725) -- (6.283,9.78) -- (6.368,9.865) -- (6.423,9.972) -- (6.442,10.091) -- (6.423,10.21) -- (6.368,10.317) -- (6.283,10.402) -- (6.176,10.457) -- (6.057,10.475) -- (6.057,10.475) -- (5.938,10.457) -- (5.831,10.402) -- (5.746,10.317) -- (5.692,10.21) -- (5.673,10.091) -- (5.692,9.972) -- (5.746,9.865) -- (5.831,9.78) -- (5.938,9.725) -- (6.057,9.706) -- cycle;
\node at (6.057,10.091) {\scalebox{1.33}{\small 1}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.361,9.082) -- (5.48,9.101) -- (5.587,9.155) -- (5.672,9.24) -- (5.727,9.347) -- (5.746,9.466) -- (5.727,9.585) -- (5.672,9.692) -- (5.587,9.777) -- (5.48,9.832) -- (5.361,9.851) -- (5.361,9.851) -- (5.242,9.832) -- (5.135,9.777) -- (5.05,9.692) -- (4.996,9.585) -- (4.977,9.466) -- (4.996,9.347) -- (5.05,9.24) -- (5.135,9.155) -- (5.242,9.101) -- (5.361,9.082) -- cycle;
\node at (5.361,9.466) {\scalebox{1.33}{\small 2}};
\filldraw[fill=white, draw=black, line width=0.5pt] (4.316,7.627) -- (4.435,7.645) -- (4.542,7.7) -- (4.627,7.785) -- (4.682,7.892) -- (4.701,8.011) -- (4.682,8.13) -- (4.627,8.237) -- (4.542,8.322) -- (4.435,8.377) -- (4.316,8.396) -- (4.316,8.396) -- (4.197,8.377) -- (4.09,8.322) -- (4.005,8.237) -- (3.951,8.13) -- (3.932,8.011) -- (3.951,7.892) -- (4.005,7.785) -- (4.09,7.7) -- (4.197,7.645) -- (4.316,7.627) -- cycle;
\node at (4.316,8.011) {\scalebox{1.33}{\small 3}};
\filldraw[fill=white, draw=black, line width=0.5pt] (2.575,9.132) -- (2.694,9.151) -- (2.801,9.206) -- (2.886,9.291) -- (2.941,9.398) -- (2.96,9.517) -- (2.941,9.635) -- (2.886,9.743) -- (2.801,9.828) -- (2.694,9.882) -- (2.575,9.901) -- (2.575,9.901) -- (2.456,9.882) -- (2.349,9.828) -- (2.264,9.743) -- (2.209,9.635) -- (2.191,9.517) -- (2.209,9.398) -- (2.264,9.291) -- (2.349,9.206) -- (2.456,9.151) -- (2.575,9.132) -- cycle;
\node at (2.575,9.517) {\scalebox{1.33}{\small 4}};
\filldraw[fill=white, draw=black, line width=0.5pt] (1.754,7.246) -- (1.873,7.265) -- (1.98,7.32) -- (2.066,7.405) -- (2.12,7.512) -- (2.139,7.631) -- (2.12,7.75) -- (2.066,7.857) -- (1.98,7.942) -- (1.873,7.997) -- (1.754,8.015) -- (1.754,8.015) -- (1.636,7.997) -- (1.528,7.942) -- (1.443,7.857) -- (1.389,7.75) -- (1.37,7.631) -- (1.389,7.512) -- (1.443,7.405) -- (1.528,7.32) -- (1.636,7.265) -- (1.754,7.246) -- cycle;
\node at (1.754,7.631) {\scalebox{1.33}{\small 5}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.681,7.738) -- (5.799,7.757) -- (5.907,7.812) -- (5.992,7.897) -- (6.046,8.004) -- (6.065,8.123) -- (6.046,8.242) -- (5.992,8.349) -- (5.907,8.434) -- (5.799,8.488) -- (5.681,8.507) -- (5.681,8.507) -- (5.562,8.488) -- (5.455,8.434) -- (5.37,8.349) -- (5.315,8.242) -- (5.296,8.123) -- (5.315,8.004) -- (5.37,7.897) -- (5.455,7.812) -- (5.562,7.757) -- (5.681,7.738) -- cycle;
\node at (5.681,8.123) {\scalebox{1.33}{\small 6}};
\filldraw[fill=white, draw=black, line width=0.5pt] (7.454,6.573) -- (7.573,6.591) -- (7.68,6.646) -- (7.765,6.731) -- (7.82,6.838) -- (7.838,6.957) -- (7.82,7.076) -- (7.765,7.183) -- (7.68,7.268) -- (7.573,7.323) -- (7.454,7.342) -- (7.454,7.342) -- (7.335,7.323) -- (7.228,7.268) -- (7.143,7.183) -- (7.088,7.076) -- (7.069,6.957) -- (7.088,6.838) -- (7.143,6.731) -- (7.228,6.646) -- (7.335,6.591) -- (7.454,6.573) -- cycle;
\node at (7.454,6.957) {\scalebox{1.33}{\small 7}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.536,5.014) -- (6.654,5.033) -- (6.762,5.087) -- (6.847,5.173) -- (6.901,5.28) -- (6.92,5.399) -- (6.901,5.517) -- (6.847,5.625) -- (6.762,5.71) -- (6.654,5.764) -- (6.536,5.783) -- (6.536,5.783) -- (6.417,5.764) -- (6.309,5.71) -- (6.224,5.625) -- (6.17,5.517) -- (6.151,5.399) -- (6.17,5.28) -- (6.224,5.173) -- (6.309,5.087) -- (6.417,5.033) -- (6.536,5.014) -- cycle;
\node at (6.536,5.399) {\scalebox{1.33}{\small 8}};
\filldraw[fill=white, draw=black, line width=0.5pt] (4.992,6.724) -- (5.111,6.743) -- (5.218,6.798) -- (5.303,6.883) -- (5.358,6.99) -- (5.376,7.109) -- (5.358,7.228) -- (5.303,7.335) -- (5.218,7.42) -- (5.111,7.474) -- (4.992,7.493) -- (4.992,7.493) -- (4.873,7.474) -- (4.766,7.42) -- (4.681,7.335) -- (4.626,7.228) -- (4.607,7.109) -- (4.626,6.99) -- (4.681,6.883) -- (4.766,6.798) -- (4.873,6.743) -- (4.992,6.724) -- cycle;
\node at (4.992,7.109) {\scalebox{1.33}{\small 9}};
\filldraw[fill=white, draw=black, line width=0.5pt] (4.736,5.011) -- (4.854,5.03) -- (4.962,5.085) -- (5.047,5.17) -- (5.101,5.277) -- (5.12,5.396) -- (5.101,5.515) -- (5.047,5.622) -- (4.962,5.707) -- (4.854,5.762) -- (4.736,5.78) -- (4.374,5.78) -- (4.255,5.762) -- (4.148,5.707) -- (4.063,5.622) -- (4.008,5.515) -- (3.989,5.396) -- (4.008,5.277) -- (4.063,5.17) -- (4.148,5.085) -- (4.255,5.03) -- (4.374,5.011) -- cycle;
\node at (4.555,5.396) {\scalebox{1.33}{\small 10}};
\filldraw[fill=white, draw=black, line width=0.5pt] (9.113,5.081) -- (9.232,5.1) -- (9.339,5.154) -- (9.424,5.239) -- (9.478,5.347) -- (9.497,5.465) -- (9.478,5.584) -- (9.424,5.692) -- (9.339,5.777) -- (9.232,5.831) -- (9.113,5.85) -- (8.751,5.85) -- (8.632,5.831) -- (8.525,5.777) -- (8.44,5.692) -- (8.385,5.584) -- (8.366,5.465) -- (8.385,5.347) -- (8.44,5.239) -- (8.525,5.154) -- (8.632,5.1) -- (8.751,5.081) -- cycle;
\node at (8.932,5.465) {\scalebox{1.33}{\small 11}};
\filldraw[fill=white, draw=black, line width=0.5pt] (2.915,5.875) -- (3.034,5.894) -- (3.141,5.948) -- (3.226,6.034) -- (3.281,6.141) -- (3.299,6.26) -- (3.281,6.378) -- (3.226,6.486) -- (3.141,6.571) -- (3.034,6.625) -- (2.915,6.644) -- (2.553,6.644) -- (2.434,6.625) -- (2.327,6.571) -- (2.242,6.486) -- (2.187,6.378) -- (2.168,6.26) -- (2.187,6.141) -- (2.242,6.034) -- (2.327,5.948) -- (2.434,5.894) -- (2.553,5.875) -- cycle;
\node at (2.734,6.26) {\scalebox{1.33}{\small 12}};
\filldraw[fill=white, draw=black, line width=0.5pt] (8.954,2.65) -- (9.072,2.668) -- (9.18,2.723) -- (9.265,2.808) -- (9.319,2.915) -- (9.338,3.034) -- (9.319,3.153) -- (9.265,3.26) -- (9.18,3.345) -- (9.072,3.4) -- (8.954,3.419) -- (8.592,3.419) -- (8.473,3.4) -- (8.366,3.345) -- (8.281,3.26) -- (8.226,3.153) -- (8.207,3.034) -- (8.226,2.915) -- (8.281,2.808) -- (8.366,2.723) -- (8.473,2.668) -- (8.592,2.65) -- cycle;
\node at (8.773,3.034) {\scalebox{1.33}{\small 13}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.241,3.291) -- (5.36,3.31) -- (5.467,3.364) -- (5.552,3.449) -- (5.606,3.556) -- (5.625,3.675) -- (5.606,3.794) -- (5.552,3.901) -- (5.467,3.986) -- (5.36,4.041) -- (5.241,4.06) -- (4.879,4.06) -- (4.76,4.041) -- (4.653,3.986) -- (4.568,3.901) -- (4.513,3.794) -- (4.494,3.675) -- (4.513,3.556) -- (4.568,3.449) -- (4.653,3.364) -- (4.76,3.31) -- (4.879,3.291) -- cycle;
\node at (5.06,3.675) {\scalebox{1.33}{\small 14}};
\filldraw[fill=white, draw=black, line width=0.5pt] (7.343,4.1) -- (7.462,4.119) -- (7.569,4.174) -- (7.654,4.259) -- (7.708,4.366) -- (7.727,4.485) -- (7.708,4.604) -- (7.654,4.711) -- (7.569,4.796) -- (7.462,4.851) -- (7.343,4.869) -- (6.981,4.869) -- (6.862,4.851) -- (6.755,4.796) -- (6.67,4.711) -- (6.615,4.604) -- (6.596,4.485) -- (6.615,4.366) -- (6.67,4.259) -- (6.755,4.174) -- (6.862,4.119) -- (6.981,4.1) -- cycle;
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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 & C, D, F, G, K, M & 6 \\ \hline
clairs & A, B, E, H, I, J, L & 7 \\ \hline
\end{tabular}
\end{center}
\noindent{\color{red!80!black}\bfseries Il y a \textbf{6} carrefours sombres et \textbf{7} clairs. Il y en a donc \textbf{1 de plus} du côté des clairs.}\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 6 carrefours sombres et 7 clairs — c'est impossible.}\par\addvspace{0.4em}
\noindent \textbf{4.}\par\addvspace{0.35em}
\noindent{\color{red!80!black}\bfseries \textbf{Non plus.} Avec un carrefour clair de plus, la tournée doit \textbf{partir et arriver} sur un carrefour clair. Or l'école est en \textbf{F}, qui est sombre.}\par\addvspace{0.4em}
\noindent{\color{green!45!black}Une tournée existe pourtant dans ce quartier : il suffirait d'installer l'école sur un carrefour clair. Ce n'est pas le plan qui est en cause, c'est l'endroit d'où l'on part.}\par\addvspace{0.4em}
\end{document}
