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\firstpageheader{}{\bf Knights and Knaves Problems To Teach Logic}{}
%\runningheader{}{\bf From Proofs to Logic (Revised)}{}
\begin{document}
Here are some Knights and Knaves puzzles that might be good for teaching concepts in logic
\begin{questions}
\question While walking through a fictional forest, you encounter three trolls guarding a bridge. Each is either a {\em knight}, who always tells the truth, or a {\em knave}, who always lies. The trolls will not let you pass until you correctly identify each as either a knight or a knave. Each troll makes a single statement:
\begin{itemize}
\item[] Troll 1: Only one of us is a knave.
\item[] Troll 2: No, only one of us is a knight.
\item[] Troll 3: We are all knaves.
\end{itemize}
Which troll is which?
\question You stumble upon two trolls playing Stratego\textsuperscript{\textregistered}. They tell you:
\begin{itemize}
\item[]Troll 1: If we are cousins, then we are both knaves.
\item[]Troll 2: We are cousins or we are both knaves.
\end{itemize}
Could both trolls be knights?
\question You come across four trolls playing bridge. They declare:
\begin{itemize}
\item[] Troll 1: All trolls here see at least one knave.
\item[] Troll 2: I see at least one troll that sees only knaves.
\item[] Troll 3: Some trolls are scared of goats.
\item[] Troll 4: All trolls are scared of goats.
\end{itemize}
Are there any trolls that are not scared of goats?
\question You encounter three more trolls:
\begin{itemize}
\item[] Troll 1: If I am a knave then there are exactly two knights here.
\item[] Troll 2: Troll 1 is lying.
\item[] Troll 3: Either we are all knaves or at least one of us is a knight.
\end{itemize}
Which troll is which?
\question You find yourself face-to-face with 13 trolls.
Luckily for you, each troll makes a statement. The trolls make almost identical statements:
\begin{quote}By the time I'm finished speaking, you will have heard $x$ of us lie to you\end{quote}
where $x$ is some number. However, no two trolls use the same number for $x$. Additionally, the first 12 trolls pick numbers for $x$ such that it is impossible to deduce whether the troll who just spoke is a knight or a knave. After hearing the statement of the 13th troll, you can deduce the status of all 13 trolls.
Which trolls are knights and which are knaves?
\end{questions}
\end{document}