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