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\pagestyle{Standard}
\title{The Princess or the Tiger}
\begin{document}
\clearpage\pagestyle{Standard}
{\selectlanguage{english}\bfseries
The Princess or the Tiger}

{\selectlanguage{english}
  from: Raymond Smullyan}


\bigskip

{\selectlanguage{english}
The King of Indrahabad had heard of a story where a prisoner had to
choose between two doors: behind one there was a princess, behind the
other a tiger. If the prisoner chose the princess, he could marry her;
if he chose the tiger, he would probably be eaten.}

{\selectlanguage{english}
The King thought this was a nice idea for his prisoners. But
he didn't want to leave things completely to chance, so he decided that
he would put some signs up on the doors. The signs would give some
clues as to what was behind the doors. A clever prisoner who can reason
logically would be able to save his own life. And, of course, in that
way the King could ensure that the husbands for all his daughters would
be smart!}

{\selectlanguage{english}
To make it a bit more difficult the King decided that it would
also be possible that there are princesses behind both doors or tigers
behind both doors. But there will never be more than one princess per
room or one tiger per room.}


\bigskip

{\selectlanguage{english}
CASE 1}

{\selectlanguage{english}
The following two signs were put up on the doors:}



\begin{center}
\begin{minipage}{2.1346in}
{\centering\selectlanguage{english}
I
\par}

{\centering\selectlanguage{english}\itshape
In one of these rooms, there is a princess and, in the other, there is a
tiger.
\par}
\end{minipage}\end{center}
\begin{center}
\begin{minipage}{2.1346in}
{\centering\selectlanguage{english}
II
\par}

{\centering\selectlanguage{english}\itshape
In this room, there is a princess and, in the other room, there is a tiger.
\par}
\end{minipage}\end{center}



\bigskip

{\selectlanguage{english}
The prisoner asked: ``Is it true, what the signs say?''}

{\selectlanguage{english}
The King said: ``One is true and one is false''.}

{\selectlanguage{english}
Which door would you take if you were the prisoner? Why?}



\begin{center}
\begin{minipage}{5.5098in}

\bigskip
\end{minipage}\end{center}

\bigskip


\bigskip


\bigskip


\bigskip

\bigskip


{\selectlanguage{english}
CASE II}

{\selectlanguage{english}
So happily the first prisoner succeeded in saving his life and
ran away with his bride. }

{\selectlanguage{english}
For the second prisoner the following signs were put up:}



\begin{center}
\begin{minipage}{2.3846in}
{\centering\selectlanguage{english}
I
\par}

{\centering\selectlanguage{english}\itshape
In the other room, there is a tiger.
\par}
\end{minipage}\end{center}
\begin{center}
\begin{minipage}{2.5098in}
{\centering\selectlanguage{english}
II
\par}

{\centering\selectlanguage{english}\itshape
In at least one of these rooms, there is a princess.
\par}
\end{minipage}\end{center}

\bigskip


{\selectlanguage{english}
``Are they true or not?'' asked the prisoner.}

{\selectlanguage{english}
``They are either both true or both false,'' said the King.}

{\selectlanguage{english}
Which room should the prisoner choose now?}

\begin{center}
\begin{minipage}{5.6346in}

\bigskip
\end{minipage}\end{center}

\bigskip

\bigskip

\bigskip 

\bigskip

\bigskip

{\selectlanguage{english}
The King decided to make it a bit more difficult because he
was tired of the prisoners running away with the princesses. He made a
new rule for the next 3 cases:}

\liststyleWWviiiNumi
\begin{enumerate}
\item {\selectlanguage{english}
If there is a princess in room I then the sign of room one would be
true. If there is a tiger in room I, then the sign will be false.}
\item {\selectlanguage{english}
For room two it's just the opposite: if there is a princess in room II,
the sign is false and if there is a tiger in room II the sign is true }
\end{enumerate}

\bigskip


\bigskip

{\selectlanguage{english}
CASE 3}

\begin{center}
\begin{minipage}{2.3846in}
{\centering\selectlanguage{english}
I
\par}

{\centering\selectlanguage{english}\itshape
In both rooms, there is a princess.
\par}
\end{minipage}\end{center}
\begin{center}
\begin{minipage}{2.2598in}
{\centering\selectlanguage{english}
II
\par}

{\centering\selectlanguage{english}\itshape
In both rooms, there is a princess.
\par}
\end{minipage}\end{center}




\bigskip

{\selectlanguage{english}
Which room should the prisoner choose and why?}



\begin{center}
\begin{minipage}{5.5098in}

\bigskip
\end{minipage}\end{center}

\bigskip


\bigskip


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\bigskip

{\selectlanguage{english}
CASE 4}

\begin{center}
\begin{minipage}{2.2598in}
{\centering\selectlanguage{english}
I
\par}

{\centering\selectlanguage{english}\itshape
In at least one room, there is a princess.
\par}
\end{minipage}\end{center}
\begin{center}
\begin{minipage}{2.3846in}
{\centering\selectlanguage{english}
II
\par}

{\centering\selectlanguage{english}\itshape
The princess is in the other room.
\par}
\end{minipage}\end{center}


\bigskip

{\selectlanguage{english}
 Which room would you choose and why?}



\begin{center}
\begin{minipage}{5.7598in}

\bigskip
\end{minipage}\end{center}

\bigskip


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\bigskip

{\selectlanguage{english}
CASE 5}

{\selectlanguage{english}
The King was very proud of these puzzles, and also of this
next one:}



\begin{center}
\begin{minipage}{2.2598in}
{\centering\selectlanguage{english}
I
\par}

{\centering\selectlanguage{english}\itshape
Whichever room you take, it makes no difference.
\par}
\end{minipage}\end{center}
\begin{center}
\begin{minipage}{2.1346in}
{\centering\selectlanguage{english}
II
\par}

{\centering\selectlanguage{english}\itshape
In the other room, there is a princess.
\par}
\end{minipage}\end{center}


\bigskip

{\selectlanguage{english}
Which room should he take and why?}

{\selectlanguage{english}
}

\begin{center}
\begin{minipage}{5.6346in}

\bigskip
\end{minipage}\end{center}
\clearpage{\selectlanguage{english}
The King was very unhappy because all his prisoners left with
one of his daughters. He decided to change his strategy. He would work
with three doors. Behind two doors, there would be a tiger, and only one
room would have a princess. Now that should make it harder!}


\bigskip

{\selectlanguage{english}
CASE 6}

\begin{center}
\begin{minipage}{2 in}
{\centering\selectlanguage{english}
I
\par}

{\centering\selectlanguage{english}\itshape
There is a tiger in room II.
\par}
\end{minipage}\end{center}
\begin{center}
\begin{minipage}{2 in}
{\centering\selectlanguage{english}
II
\par}

{\centering\selectlanguage{english}\itshape
In this room, there is a princess.
\par}
\end{minipage}\end{center}
\begin{center}
\begin{minipage}{2 in}
{\centering\selectlanguage{english}
III
\par}

{\centering\selectlanguage{english}\itshape
In this room, there is a tiger.
\par}
\end{minipage}\end{center}


\bigskip

{\selectlanguage{english}
The king told the prisoner that at most one of the signs was
true.}

{\selectlanguage{english}
Which room should the prisoner choose and why?}

\begin{center}
\begin{minipage}{5.8846in}

\bigskip
\end{minipage}\end{center}

\bigskip


\bigskip


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\bigskip


\bigskip

{\selectlanguage{english}
CASE 7}



\begin{center}
\begin{minipage}{2in}
{\centering\selectlanguage{english}
I
\par}
There is a tiger in room II.
{\centering\selectlanguage{english}\itshape

\par}
\end{minipage}\end{center}
\begin{center}
\begin{minipage}{2in}
{\centering\selectlanguage{english}
II
\par}

{\centering\selectlanguage{english}\itshape
There is a tiger in this room.
\par}
\end{minipage}\end{center}
\begin{center}
\begin{minipage}{2in}
{\centering\selectlanguage{english}
III
\par}

{\centering\selectlanguage{english}\itshape
There is a tiger in room I.
\par}
\end{minipage}\end{center}


\bigskip

{\selectlanguage{english}
The King told the prisoner that the sign on the room of the
princess was true, and that at least one of the other signs was not
true.}

{\selectlanguage{english}
What should the prisoner do and why?}



\begin{center}
\begin{minipage}{6.1346in}

\bigskip
\end{minipage}\end{center}

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{\selectlanguage{english}\bfseries
Two More Puzzles about Hats and Very Smart Women}


\bigskip

{\selectlanguage{english}\mdseries\upshape
CASE 1}


\bigskip

{\selectlanguage{english}
\textcolor{black}{ Three very smart women are standing in a line,
and all of them are facing the same direction. The Mad Hatter has three
blue hats and two red hats and he randomly puts one hat on each woman's
head. The women knew that the Mad Hatter started with three blue hats and
two red hats, but they do not know which two hats were left over. The
woman in the back of the line can see the hats of the two women in front of
her, but she cannot see her own hat. The second woman in line can see the
hat of the woman in front of her, but she cannot see her own hat or the
hat of the woman behind her. The woman in front of the line cannot see any
hats.}}

{\selectlanguage{english}
\textcolor{black}{First, the woman in the back of the line was
asked if she could determine what color hat she was wearing, and she said
he could not. Next, the second woman in line was asked if she could
determine what color hat she was wearing, and she also said she could not.
Finally, the woman in the front of the line, who had heard what the last
two women had said, said that she knew what color hat she was wearing. What
color was it and how did she know?}}

{\selectlanguage{english}\bfseries
}

\begin{center}
\begin{minipage}{6.1346in}

\bigskip
\end{minipage}\end{center}

\bigskip


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\bigskip

{\selectlanguage{english}\mdseries\upshape\color{black}
CASE 2}


\bigskip

{\selectlanguage{english}\mdseries\color{black}
Three women are sitting in a circle, all facing one another.
Once again, the Mad Hatter has three blue hats and two red hats. The
Mad Hatter shows the women the hats and then blindfolds them. He randomly
puts one hat on each woman's head, and takes the last two hats out of the
room. Then women are told that the first one who can identify the color
of her own hat will win one million dollars, but if a woman guesses the
wrong color hat, she will have to pay one million dollars. The
blindfolds are then removed, and the women sit, staring at one another.
Finally, after a bit, one of the women exclaims ''I know what color my hat is!'' What
color was it, and how did she know?}

{\selectlanguage{english}
}
\begin{center}
\begin{minipage}{6.1346in}

\bigskip
\end{minipage}\end{center}
\end{document}
