Yet another question.

1 files changed, 62 insertions, 0 deletions

diff --git a/controle-2020qcm.tex b/controle-2020qcm.tex
index 0ea03cb..dd09605 100644
--- a/controle-2020qcm.tex
+++ b/controle-2020qcm.tex
@@ -859,6 +859,68 @@ $4$
 
 \begin{question}
 
+Quel joueur a une stratégie gagnante dans le jeu combinatoire
+(impartial, à information parfaite) associé au graphe orienté
+acyclique représenté ci-dessous, la position de départ étant
+notée $s$ ?
+
+\begin{center}
+\begin{tikzpicture}[>=stealth,thick,text width=5bp,text height=5bp,text depth=0bp]
+\node (l0) at (-40bp,0bp) [draw,circle] {};
+\node (c0) at (0bp,0bp) [draw,circle] {};
+\node (r0) at (40bp,0bp) [draw,circle] {};
+\node (l1) at (-40bp,-40bp) [draw,circle] {};
+\node (c1) at (0bp,-40bp) [draw,circle] {};
+\node (r1) at (40bp,-40bp) [draw,circle] {};
+\node (l2) at (-40bp,-80bp) [draw,circle] {};
+\node (c2) at (0bp,-80bp) [draw,circle] {};
+\node (r2) at (40bp,-80bp) [draw,circle] {};
+\node (l3) at (-40bp,-120bp) [draw,circle] {};
+\node (c3) at (0bp,-120bp) [draw,circle] {};
+\node (r3) at (40bp,-120bp) [draw,circle] {};
+\node (l4) at (-40bp,-160bp) [draw,circle] {};
+\node (c4) at (0bp,-160bp) [draw,circle] {};
+\node (r4) at (40bp,-160bp) [draw,circle] {};
+\node (c5) at (0bp,-200bp) [draw,circle] {$s$};
+\draw[->] (l0) -- (c0);  \draw[->] (r0) -- (c0);
+\draw[->] (l1) -- (l0);  \draw[->] (l1) -- (c0);
+\draw[->] (c1) -- (l0);  \draw[->] (c1) -- (r0);
+\draw[->] (r1) -- (r0);  \draw[->] (r1) -- (c0);
+\draw[->] (l1) -- (c1);  \draw[->] (r1) -- (c1);
+\draw[->] (l2) -- (l1);  \draw[->] (l2) -- (c1);
+\draw[->] (c2) -- (l1);  \draw[->] (c2) -- (r1);
+\draw[->] (r2) -- (r1);  \draw[->] (r2) -- (c1);
+\draw[->] (l2) -- (c2);  \draw[->] (r2) -- (c2);
+\draw[->] (l3) -- (l2);  \draw[->] (l3) -- (c2);
+\draw[->] (c3) -- (l2);  \draw[->] (c3) -- (r2);
+\draw[->] (r3) -- (r2);  \draw[->] (r3) -- (c2);
+\draw[->] (l3) -- (c3);  \draw[->] (r3) -- (c3);
+\draw[->] (l4) -- (l3);  \draw[->] (l4) -- (c3);
+\draw[->] (c4) -- (l3);  \draw[->] (c4) -- (r3);
+\draw[->] (r4) -- (r3);  \draw[->] (r4) -- (c3);
+\draw[->] (l4) -- (c4);  \draw[->] (r4) -- (c4);
+\draw[->] (c5) -- (l4);  \draw[->] (c5) -- (r4);
+\end{tikzpicture}
+\end{center}
+
+\rightanswer
+le second joueur
+
+\answer
+le premier joueur
+
+\answer
+aucun des deux
+
+\end{question}
+
+
+%
+%
+%
+
+\begin{question}
+
 Alice et Bob jouent au jeu suivant sur un échiquier $8\times 8$ sur
 lequel est positionné un unique pion (commun aux deux joueurs) :
 \begin{itemize}