Added retrograde handout

Advanced/Retrograde Analysis/parts/hard.tex

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+% Arabian Knights 5
+\problem{The hidden castle}
+\difficulty{7}{7}
+
+There is a white castle hidden on this board. Where is it? \par
+None of the royalty has moved or been under attack. \par
+
+\manyboards{
+	nb8,qd8,ke8,ng8,rh8,
+	pa7,pb7,pc7,pf7,pg7,
+	pe6,pf6,ph6,
+	Pa4,Bc4,Pe4,
+	Pc3,
+	Pb2,Pd2,Pf2,Pg2,
+	Qd1,Ke1
+}
+
+\begin{solution}
+	See \say{The Hidden Castle} in \textit{The Chess Mysteries of the Arabian Knights}.
+\end{solution}
+
+\vfill
+\pagebreak
+
+
+
+% Arabian Knights 6
+\problem{Who moved last?}
+\difficulty{7}{7}
+
+After many moves of chess, the board looks as follows. \par
+Who moved last? \par
+
+\manyboards{
+	ka8,Kc8,bf8,rh8,
+	pb7,pc7,pf7,pg7,
+	Ba6,
+	Pe4,
+	Pa2,Pb2,Pd2,Pg2,Ph2,
+	Ra1,Nb1,Bc1,Qd1,Rh1
+}
+
+\begin{solution}
+	See \say{A Vital Decision} in \textit{The Chess Mysteries of the Arabian Knights}.
+\end{solution}
+
+\vfill
+\pagebreak
+
+
+
+
+% Arabian Knights 3
+\problem{The king in disguise}<kingdisguise>
+\difficulty{7}{7}
+
+The white king is exploring his kingdom under a disguise. He could look like any piece of any color.\par
+Show that he must be on C7.
+
+\manyboards{
+	qa8,nb8,be8,Qg8,kh8,
+	pa7,Pb7,pc7,Nd7,pe7,Pf7,ph7,
+	pa6,Pc6,Pg6,
+	ra5,pb5,Rd5,Ph5,
+	Pa4,Nc4,Pe4,Bg4
+}
+
+\begin{solution}
+	Black is in check, so we know that it is Black's move and White is not in check.\par
+	Assume the white king is not on C7. Where else could he hide?
+	First, we exclude the black pawns on A6, A7, and B5, since the white king would be in check in any of those positions. \par
+	
+	\vspace{2mm}
+
+	The pawn on A6 came from B7 by capturing one piece, and the pawn on B5 came from D7 by capturing two.
+	(Note that this may not be true if we don't assume the pawn on C7 is real.)
+	We've counted three captures, all on white squares, so the white black-square bishop must have been captured seperately.
+
+	\vspace{2mm}
+
+	Thus, at least four white pieces have been captured. White has 12 pieces on the board,
+	so the white king must be disguised as a white piece if he isn't on C7.
+	If we Exclude a few more pieces in check, we now see that the white king must
+	be on D5, E4, G4, or H5 if he isn't on C7.
+
+	\linehack{}
+
+	The white queen has to have moved from F8 to capture a piece on G8 to put Black in check. What was Black's move before this?
+	It couldn't have been the king from G7, since the white queen wouldn't have been able to enter F8.
+	It couldn't have been any other piece on the board, since they are all trapped.
+	So, Black's last move must have been with the mystery piece on G8.
+
+	\vspace{2mm}
+
+	Where did it come from? This piece can't be a bishop (how would it get in?), so it must be a queen, rook, or knight.
+	If it is a queen or rook, it must have come from G7, which is impossible---the white queen wouldn't be able to get in.
+	The mystery piece must therefore be a knight. It couldn't have come from H6 (again, the queen couldn't have gotten in to deliver a check),
+	so it must have come from F6.
+
+	\linehack{}
+
+	We now know that the white king is not on D5, E4, G4, or H5, since all those were in check when the black knight was on F6.
+	However, the white king must be on one of those four squares if he isn't on C7. This is a contradiction --- therefore the king must be hiding on C7.
+
+\end{solution}
+
+\vfill
+\pagebreak
+
+
+
+% Arabian Knights 3
+\problem{The king in disguise once more}
+\difficultynote{2}{5}{(Assuming you've solved \ref{kingdisguise})}
+
+The white king is again exploring his kingdom, now under a different disguise. Where is he? \par
+\hint{\say{different disguise} implies that the white king looks like a different piece!}
+
+\manyboards{
+	nb8,be8,Qg8,kh8,
+	pa7,Pb7,pc7,Nd7,pe7,Pf7,ph7,
+	pa6,Pc6,Pg6,
+	ra5,pb5,Rd5,Ph5,
+	Pa4,Nc4,Pe4,Bg4
+}
+
+\begin{solution}
+	Use the same arguments as before, but now assume that the king isn't a black pawn.
+
+	\vspace{2mm}
+
+	Again, the king is disguised as a white piece, and must be on D5, E4, G4, H5, or B7. \par
+	For the same reasons as above, he can't be on D5, E4, G4, or H5, so he must be on B7.
+\end{solution}
+
+\vfill
+\pagebreak