A http://en.wikipedia.org/wiki/Mis%C3%A8re#Mis.C3.A8re_game is a game played by the regular rules with one change; whoever wins the game according the regular rules is the loser. Consider again the game of \emph{Scoring}, but this time we'll play it as a misere game.

1. For which values of $n$ does the first player have a winning strategy when playing misere, provided each player must take 1, 2, or 3 objects.?
2. For which values of $n$ does the first player have a winning strategy when playing misere, provided each player must take 1, 2, 3, or 4 objects.?
3. If instead a player must take between 1 and $k$ objects, conjecture the values of $n$ for which the first player has a winning strategy when playing misere.

• Make remarks with a list.

problem.the_game_of_scoring_misere.tex

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% DEPENDENCIES
% RequiredPackages: \usepackage{tikz}
% RequiredMacros: \DeclareMathOperator{\aut}{Aut} 
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\begin{problem}
%The Game of Scoring Misere
\item A misere game is a game played by the regular rules with one change; whoever wins the game according the regular rules is the loser. Consider again the game of \emph{Scoring}, but this time we'll play it as a misere game. 
 \begin{enumerate}
  \item For which values of $n$ does the first player have a winning strategy when playing misere, provided each player must take 1, 2, or 3 objects.? 
  \item For which values of $n$ does the first player have a winning strategy when playing misere, provided each player must take 1, 2, 3, or 4 objects.? 
  \item If instead a player must take between 1 and $k$ objects, conjecture the values of $n$ for which the first player has a winning strategy when playing misere.
 \end{enumerate}
\end{problem}

• Dihedral group

problem