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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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\noindent \textbf{Le car part de l'école, au carrefour E, 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 chemin Creux & Ⓑ Place Sainte-Croix & Ⓛ Coin du Lavoir \\ \hline
① quai aux Fleurs & ⑪ chemin de Ronde & Ⓒ Place de l'Église & Ⓜ Rond-point du Stade \\ \hline
② rue Neuve & ⑫ rue du Moulin & Ⓓ Carrefour de la Mairie & \cellcolor{black!32}\bfseries Les bâtiments \\ \hline
③ rue de l'Église & ⑬ passage du Marché & Ⓔ Rond-point de la Poste & \textbf{a} l'école \\ \hline
④ impasse des Roses & ⑭ rue du Four & Ⓕ Carrefour des Tilleuls & \textbf{b} la bibliothèque \\ \hline
⑤ rue de la Mairie & ⑮ rue Basse & Ⓖ Rond-point des Vaches & \textbf{c} le stade \\ \hline
⑥ rue du Puits & ⑯ rue Haute & Ⓗ Fontaine Notre-Dame & \textbf{d} la gendarmerie \\ \hline
⑦ rue des Lilas & ⑰ chemin des Vignes & Ⓘ Placette des Ormes &  \\ \hline
⑧ rue de la Poste & \cellcolor{black!32}\bfseries Les carrefours & Ⓙ Place du Vieux-Puits &  \\ \hline
⑨ rue Verte & Ⓐ Carrefour de l'Hôpital & Ⓚ Rond-point de la Gare &  \\ \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] (1.36,4.809) -- (1.609,4.784) -- (1.859,4.765) -- (2.11,4.751) -- (2.36,4.744) -- (2.611,4.743) -- (2.861,4.747) -- (3.112,4.757) -- (3.362,4.773) -- (3.612,4.795) -- (3.861,4.823) -- (4.11,4.857) -- (4.357,4.896) -- (4.603,4.942) -- (4.849,4.993);
\draw[line width=0.5pt] (1.36,4.809) -- (1.423,4.624) -- (1.481,4.437) -- (1.535,4.249) -- (1.584,4.06) -- (1.629,3.87) -- (1.67,3.678) -- (1.706,3.486) -- (1.737,3.293) -- (1.764,3.099) -- (1.786,2.905) -- (1.804,2.71) -- (1.817,2.515) -- (1.826,2.32) -- (1.829,2.124);
\draw[line width=0.5pt] (7.789,2.332) -- (8.043,2.298) -- (8.297,2.27) -- (8.553,2.248) -- (8.809,2.232) -- (9.065,2.222) -- (9.321,2.218) -- (9.578,2.221) -- (9.834,2.229) -- (10.09,2.243) -- (10.345,2.263) -- (10.6,2.29) -- (10.855,2.322) -- (11.108,2.36) -- (11.36,2.404);
\draw[line width=0.5pt] (1.829,2.124) -- (2.015,2.111) -- (2.2,2.092) -- (2.385,2.07) -- (2.569,2.043) -- (2.753,2.011) -- (2.935,1.976) -- (3.117,1.936) -- (3.298,1.892) -- (3.478,1.843) -- (3.657,1.791) -- (3.834,1.734) -- (4.01,1.673) -- (4.184,1.608) -- (4.357,1.539);
\draw[line width=0.5pt] (4.357,1.539) -- (4.609,1.558) -- (4.86,1.582) -- (5.111,1.613) -- (5.361,1.649) -- (5.61,1.692) -- (5.858,1.74) -- (6.105,1.794) -- (6.351,1.854) -- (6.595,1.919) -- (6.838,1.99) -- (7.079,2.067) -- (7.317,2.15) -- (7.554,2.238) -- (7.789,2.332);
\filldraw[fill=black!38, draw=black, line width=0.5pt] (4.922,11.523) -- (4.893,11.666) -- (4.812,11.787) -- (4.691,11.868) -- (4.548,11.896) -- (4.405,11.868) -- (4.284,11.787) -- (4.204,11.666) -- (4.175,11.523) -- (4.204,11.38) -- (4.284,11.259) -- (4.405,11.178) -- (4.548,11.15) -- (4.691,11.178) -- (4.812,11.259) -- (4.893,11.38) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (8.078,11.424) -- (8.05,11.567) -- (7.969,11.688) -- (7.848,11.769) -- (7.705,11.797) -- (7.562,11.769) -- (7.441,11.688) -- (7.36,11.567) -- (7.332,11.424) -- (7.36,11.281) -- (7.441,11.16) -- (7.562,11.079) -- (7.705,11.051) -- (7.848,11.079) -- (7.969,11.16) -- (8.05,11.281) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (1.827,11.349) -- (1.799,11.491) -- (1.718,11.613) -- (1.597,11.693) -- (1.454,11.722) -- (1.311,11.693) -- (1.19,11.613) -- (1.109,11.491) -- (1.081,11.349) -- (1.109,11.206) -- (1.19,11.085) -- (1.311,11.004) -- (1.454,10.975) -- (1.597,11.004) -- (1.718,11.085) -- (1.799,11.206) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (4.912,8.683) -- (4.884,8.826) -- (4.803,8.947) -- (4.682,9.028) -- (4.539,9.056) -- (4.396,9.028) -- (4.275,8.947) -- (4.194,8.826) -- (4.166,8.683) -- (4.194,8.54) -- (4.275,8.419) -- (4.396,8.338) -- (4.539,8.31) -- (4.682,8.338) -- (4.803,8.419) -- (4.884,8.54) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (8.543,8.277) -- (8.514,8.419) -- (8.433,8.541) -- (8.312,8.621) -- (8.169,8.65) -- (8.027,8.621) -- (7.906,8.541) -- (7.825,8.419) -- (7.796,8.277) -- (7.825,8.134) -- (7.906,8.013) -- (8.027,7.932) -- (8.169,7.903) -- (8.312,7.932) -- (8.433,8.013) -- (8.514,8.134) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (7.862,5.27) -- (7.833,5.413) -- (7.752,5.534) -- (7.631,5.615) -- (7.489,5.644) -- (7.346,5.615) -- (7.225,5.534) -- (7.144,5.413) -- (7.115,5.27) -- (7.144,5.128) -- (7.225,5.007) -- (7.346,4.926) -- (7.489,4.897) -- (7.631,4.926) -- (7.752,5.007) -- (7.833,5.128) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (5.222,4.993) -- (5.193,5.136) -- (5.113,5.257) -- (4.991,5.338) -- (4.849,5.366) -- (4.706,5.338) -- (4.585,5.257) -- (4.504,5.136) -- (4.475,4.993) -- (4.504,4.85) -- (4.585,4.729) -- (4.706,4.648) -- (4.849,4.62) -- (4.991,4.648) -- (5.113,4.729) -- (5.193,4.85) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (11.109,4.827) -- (11.081,4.97) -- (11.0,5.091) -- (10.879,5.172) -- (10.736,5.2) -- (10.593,5.172) -- (10.472,5.091) -- (10.391,4.97) -- (10.363,4.827) -- (10.391,4.684) -- (10.472,4.563) -- (10.593,4.482) -- (10.736,4.454) -- (10.879,4.482) -- (11.0,4.563) -- (11.081,4.684) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (1.733,4.809) -- (1.705,4.952) -- (1.624,5.073) -- (1.503,5.154) -- (1.36,5.182) -- (1.217,5.154) -- (1.096,5.073) -- (1.015,4.952) -- (0.987,4.809) -- (1.015,4.666) -- (1.096,4.545) -- (1.217,4.464) -- (1.36,4.436) -- (1.503,4.464) -- (1.624,4.545) -- (1.705,4.666) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (11.733,2.404) -- (11.705,2.547) -- (11.624,2.668) -- (11.503,2.749) -- (11.36,2.777) -- (11.217,2.749) -- (11.096,2.668) -- (11.015,2.547) -- (10.987,2.404) -- (11.015,2.261) -- (11.096,2.14) -- (11.217,2.059) -- (11.36,2.031) -- (11.503,2.059) -- (11.624,2.14) -- (11.705,2.261) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (8.162,2.332) -- (8.134,2.474) -- (8.053,2.596) -- (7.932,2.676) -- (7.789,2.705) -- (7.646,2.676) -- (7.525,2.596) -- (7.444,2.474) -- (7.416,2.332) -- (7.444,2.189) -- (7.525,2.068) -- (7.646,1.987) -- (7.789,1.958) -- (7.932,1.987) -- (8.053,2.068) -- (8.134,2.189) -- cycle;
\filldraw[fill=black!38, draw=black, line width=0.5pt] (2.203,2.124) -- (2.174,2.267) -- (2.093,2.388) -- (1.972,2.469) -- (1.829,2.498) -- (1.687,2.469) -- (1.566,2.388) -- (1.485,2.267) -- (1.456,2.124) -- (1.485,1.982) -- (1.566,1.86) -- (1.687,1.78) -- (1.829,1.751) -- (1.972,1.78) -- (2.093,1.86) -- (2.174,1.982) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (4.73,1.539) -- (4.701,1.682) -- (4.621,1.803) -- (4.499,1.884) -- (4.357,1.912) -- (4.214,1.884) -- (4.093,1.803) -- (4.012,1.682) -- (3.983,1.539) -- (4.012,1.396) -- (4.093,1.275) -- (4.214,1.194) -- (4.357,1.166) -- (4.499,1.194) -- (4.621,1.275) -- (4.701,1.396) -- cycle;
\filldraw[fill=white, draw=black, line width=0.5pt] (6.135,11.343) -- (6.253,11.362) -- (6.361,11.416) -- (6.446,11.502) -- (6.5,11.609) -- (6.519,11.728) -- (6.5,11.846) -- (6.446,11.954) -- (6.361,12.039) -- (6.253,12.093) -- (6.135,12.112) -- (6.135,12.112) -- (6.016,12.093) -- (5.909,12.039) -- (5.824,11.954) -- (5.769,11.846) -- (5.75,11.728) -- (5.769,11.609) -- (5.824,11.502) -- (5.909,11.416) -- (6.016,11.362) -- (6.135,11.343) -- cycle;
\node at (6.135,11.728) {\scalebox{1.615}{\small 1}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.045,9.717) -- (5.164,9.735) -- (5.271,9.79) -- (5.356,9.875) -- (5.411,9.982) -- (5.43,10.101) -- (5.411,10.22) -- (5.356,10.327) -- (5.271,10.412) -- (5.164,10.467) -- (5.045,10.486) -- (5.045,10.486) -- (4.926,10.467) -- (4.819,10.412) -- (4.734,10.327) -- (4.68,10.22) -- (4.661,10.101) -- (4.68,9.982) -- (4.734,9.875) -- (4.819,9.79) -- (4.926,9.735) -- (5.045,9.717) -- cycle;
\node at (5.045,10.101) {\scalebox{1.615}{\small 2}};
\filldraw[fill=white, draw=black, line width=0.5pt] (8.188,9.503) -- (8.307,9.522) -- (8.414,9.576) -- (8.499,9.661) -- (8.554,9.768) -- (8.572,9.887) -- (8.554,10.006) -- (8.499,10.113) -- (8.414,10.198) -- (8.307,10.253) -- (8.188,10.272) -- (8.188,10.272) -- (8.069,10.253) -- (7.962,10.198) -- (7.877,10.113) -- (7.822,10.006) -- (7.803,9.887) -- (7.822,9.768) -- (7.877,9.661) -- (7.962,9.576) -- (8.069,9.522) -- (8.188,9.503) -- cycle;
\node at (8.188,9.887) {\scalebox{1.615}{\small 3}};
\filldraw[fill=white, draw=black, line width=0.5pt] (2.972,11.563) -- (3.091,11.582) -- (3.198,11.636) -- (3.283,11.721) -- (3.338,11.828) -- (3.357,11.947) -- (3.338,12.066) -- (3.283,12.173) -- (3.198,12.258) -- (3.091,12.313) -- (2.972,12.332) -- (2.972,12.332) -- (2.854,12.313) -- (2.746,12.258) -- (2.661,12.173) -- (2.607,12.066) -- (2.588,11.947) -- (2.607,11.828) -- (2.661,11.721) -- (2.746,11.636) -- (2.854,11.582) -- (2.972,11.563) -- cycle;
\node at (2.972,11.947) {\scalebox{1.615}{\small 4}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.38,8.328) -- (6.499,8.346) -- (6.606,8.401) -- (6.691,8.486) -- (6.746,8.593) -- (6.765,8.712) -- (6.746,8.831) -- (6.691,8.938) -- (6.606,9.023) -- (6.499,9.078) -- (6.38,9.097) -- (6.38,9.097) -- (6.261,9.078) -- (6.154,9.023) -- (6.069,8.938) -- (6.014,8.831) -- (5.996,8.712) -- (6.014,8.593) -- (6.069,8.486) -- (6.154,8.401) -- (6.261,8.346) -- (6.38,8.328) -- cycle;
\node at (6.38,8.712) {\scalebox{1.615}{\small 5}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.229,6.498) -- (5.348,6.517) -- (5.455,6.572) -- (5.54,6.657) -- (5.595,6.764) -- (5.614,6.883) -- (5.595,7.002) -- (5.54,7.109) -- (5.455,7.194) -- (5.348,7.249) -- (5.229,7.267) -- (5.229,7.267) -- (5.11,7.249) -- (5.003,7.194) -- (4.918,7.109) -- (4.863,7.002) -- (4.845,6.883) -- (4.863,6.764) -- (4.918,6.657) -- (5.003,6.572) -- (5.11,6.517) -- (5.229,6.498) -- cycle;
\node at (5.229,6.883) {\scalebox{1.615}{\small 6}};
\filldraw[fill=white, draw=black, line width=0.5pt] (8.08,6.332) -- (8.199,6.351) -- (8.306,6.406) -- (8.391,6.491) -- (8.446,6.598) -- (8.465,6.717) -- (8.446,6.835) -- (8.391,6.943) -- (8.306,7.028) -- (8.199,7.082) -- (8.08,7.101) -- (8.08,7.101) -- (7.961,7.082) -- (7.854,7.028) -- (7.769,6.943) -- (7.714,6.835) -- (7.695,6.717) -- (7.714,6.598) -- (7.769,6.491) -- (7.854,6.406) -- (7.961,6.351) -- (8.08,6.332) -- cycle;
\node at (8.08,6.717) {\scalebox{1.615}{\small 7}};
\filldraw[fill=white, draw=black, line width=0.5pt] (9.182,5.179) -- (9.301,5.198) -- (9.409,5.253) -- (9.494,5.338) -- (9.548,5.445) -- (9.567,5.564) -- (9.548,5.682) -- (9.494,5.79) -- (9.409,5.875) -- (9.301,5.929) -- (9.182,5.948) -- (9.182,5.948) -- (9.064,5.929) -- (8.956,5.875) -- (8.871,5.79) -- (8.817,5.682) -- (8.798,5.564) -- (8.817,5.445) -- (8.871,5.338) -- (8.956,5.253) -- (9.064,5.198) -- (9.182,5.179) -- cycle;
\node at (9.182,5.564) {\scalebox{1.615}{\small 8}};
\filldraw[fill=white, draw=black, line width=0.5pt] (7.9,3.443) -- (8.019,3.462) -- (8.126,3.517) -- (8.211,3.602) -- (8.266,3.709) -- (8.284,3.828) -- (8.266,3.947) -- (8.211,4.054) -- (8.126,4.139) -- (8.019,4.193) -- (7.9,4.212) -- (7.9,4.212) -- (7.781,4.193) -- (7.674,4.139) -- (7.589,4.054) -- (7.534,3.947) -- (7.515,3.828) -- (7.534,3.709) -- (7.589,3.602) -- (7.674,3.517) -- (7.781,3.462) -- (7.9,3.443) -- cycle;
\node at (7.9,3.828) {\scalebox{1.615}{\small 9}};
\filldraw[fill=white, draw=black, line width=0.5pt] (6.298,5.239) -- (6.417,5.257) -- (6.524,5.312) -- (6.609,5.397) -- (6.664,5.504) -- (6.682,5.623) -- (6.664,5.742) -- (6.609,5.849) -- (6.524,5.934) -- (6.417,5.989) -- (6.298,6.008) -- (5.936,6.008) -- (5.817,5.989) -- (5.71,5.934) -- (5.625,5.849) -- (5.57,5.742) -- (5.551,5.623) -- (5.57,5.504) -- (5.625,5.397) -- (5.71,5.312) -- (5.817,5.257) -- (5.936,5.239) -- cycle;
\node at (6.117,5.623) {\scalebox{1.615}{\small 10}};
\filldraw[fill=white, draw=black, line width=0.5pt] (5.022,2.848) -- (5.141,2.866) -- (5.248,2.921) -- (5.333,3.006) -- (5.388,3.113) -- (5.406,3.232) -- (5.388,3.351) -- (5.333,3.458) -- (5.248,3.543) -- (5.141,3.598) -- (5.022,3.617) -- (4.66,3.617) -- (4.541,3.598) -- (4.434,3.543) -- (4.349,3.458) -- (4.294,3.351) -- (4.275,3.232) -- (4.294,3.113) -- (4.349,3.006) -- (4.434,2.921) -- (4.541,2.866) -- (4.66,2.848) -- cycle;
\node at (4.841,3.232) {\scalebox{1.615}{\small 11}};
\filldraw[fill=white, draw=black, line width=0.5pt] (10.957,3.161) -- (11.075,3.18) -- (11.183,3.234) -- (11.268,3.319) -- (11.322,3.427) -- (11.341,3.545) -- (11.322,3.664) -- (11.268,3.771) -- (11.183,3.856) -- (11.075,3.911) -- (10.957,3.93) -- (10.595,3.93) -- (10.476,3.911) -- (10.369,3.856) -- (10.284,3.771) -- (10.229,3.664) -- (10.21,3.545) -- (10.229,3.427) -- (10.284,3.319) -- (10.369,3.234) -- (10.476,3.18) -- (10.595,3.161) -- cycle;
\node at (10.776,3.545) {\scalebox{1.615}{\small 12}};
\filldraw[fill=white, draw=black, line width=0.5pt] (3.273,4.757) -- (3.392,4.775) -- (3.499,4.83) -- (3.584,4.915) -- (3.638,5.022) -- (3.657,5.141) -- (3.638,5.26) -- (3.584,5.367) -- (3.499,5.452) -- (3.392,5.507) -- (3.273,5.526) -- (2.911,5.526) -- (2.792,5.507) -- (2.685,5.452) -- (2.6,5.367) -- (2.545,5.26) -- (2.526,5.141) -- (2.545,5.022) -- (2.6,4.915) -- (2.685,4.83) -- (2.792,4.775) -- (2.911,4.757) -- cycle;
\node at (3.092,5.141) {\scalebox{1.615}{\small 13}};
\filldraw[fill=white, draw=black, line width=0.5pt] (2.265,3.168) -- (2.384,3.187) -- (2.491,3.241) -- (2.576,3.326) -- (2.631,3.434) -- (2.65,3.552) -- (2.631,3.671) -- (2.576,3.778) -- (2.491,3.863) -- (2.384,3.918) -- (2.265,3.937) -- (1.903,3.937) -- (1.785,3.918) -- (1.677,3.863) -- (1.592,3.778) -- (1.538,3.671) -- (1.519,3.552) -- (1.538,3.434) -- (1.592,3.326) -- (1.677,3.241) -- (1.785,3.187) -- (1.903,3.168) -- cycle;
\node at (2.084,3.552) {\scalebox{1.615}{\small 14}};
\filldraw[fill=white, draw=black, line width=0.5pt] (9.751,2.221) -- (9.869,2.239) -- (9.977,2.294) -- (10.062,2.379) -- (10.116,2.486) -- (10.135,2.605) -- (10.116,2.724) -- (10.062,2.831) -- (9.977,2.916) -- (9.869,2.971) -- (9.751,2.99) -- (9.389,2.99) -- (9.27,2.971) -- (9.163,2.916) -- (9.078,2.831) -- (9.023,2.724) -- (9.004,2.605) -- (9.023,2.486) -- (9.078,2.379) -- (9.163,2.294) -- (9.27,2.239) -- (9.389,2.221) -- cycle;
\node at (9.57,2.605) {\scalebox{1.615}{\small 15}};
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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, E, G, H, K, L & 6 \\ \hline
clairs & B, C, D, F, I, J, M & 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{E}, 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}
