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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

369.0. "Anyone for Chess puzzles?" by METOO::YARBROUGH () Wed Oct 30 1985 15:04

Here's a logic puzzle built on the rules of Chess, by Raymond Smullyan, 
taken from the cover of his book The Chess Adventures of the Arabian 
Knights.

	+---+---+---+---+---+---+---+---+
	|   |   |   |   |   |   |   |   |  The White King is invisible but 
	+---+---+---+---+---+---+---+---+
	|   |   |   |   |   |   |   |   |  on the board somewhere. What
	+---+---+---+---+---+---+---+---+
	|   |   |   |   |   |   |   |   |  square is it on?
	+---+---+---+---+---+---+---+---+
	|   | r |   | b |   |   |   |   |  (White = uppercase, 
	+---+---+---+---+---+---+---+---+
	| B |   |   |   |   |   |   |   |  Black = lowercase)
	+---+---+---+---+---+---+---+---+
	|   |   |   |   |   |   |   |   |
	+---+---+---+---+---+---+---+---+
	|   |   |   |   |   |   |   |   |
	+---+---+---+---+---+---+---+---+
	|   |   |   | k |   |   |   |   |
	+---+---+---+---+---+---+---+---+
T.RTitleUserPersonal
Name		DateLines
369.1TLE::BRETTWed Oct 30 1985 16:463
Assuming, I presume, its black's move...

/Bevin
369.2BEING::POSTPISCHILThu Oct 31 1985 07:4728
I cannot see any way the situation shown can occur in a chess game, unless the
white bishop is on the back row and reached it by being a pawn which moved
forward and was promoted.  This would allow the king to be in many places. 

Perhaps somebody can tell me where my reasoning is faulty:  Clearly, the white
king cannot be adjacent to the black king.  Suppose it is on the other square
along the diagonal between the white bishop and the black king.  But then it is
in check from the black rook and the bishop.  The only way a king can be
attacked by two pieces is if at least one of them was revealed by the previous
move.  But no move could accomplish that.  Therefore the white king is not on
that square, so both squares along the diagonal from the white bishop to the
black king are empty, so the black king is in check.  Hence it is black's move.
On the move just completed, white must have caused the check.  The bishop cannot
have been moved to where it is, unless the black king were already in check
(hence checkmate would have already occurred) or the bishop were promoted from a
pawn.  Assuming no promotion occurred, the check of the black king is a revealed
check.  But then the white king must have been on one of the squares between the
white bishop and the black king.  It could not have been adjacent to the king,
so it must have been adjacent to the white bishop.  But this is the situation
just discarded above, unless there was something different about the board.  The
only possible difference would be another piece, which the white king captured
in making its move.  However, no possible placement of another piece to be
captured eliminates the problems with the attacks by the rook and the bishop, so
this situation is impossible. 


				-- edp
369.3TOOLS::YARBROUGHThu Oct 31 1985 08:329
The board is in 'newspaper' position, the White pieces starting at the bottom,
the Black at the top.

re .1: whose move it is can be deduced; see .2.

re .2: the argument is ALMOST correct. A hint: in the complete argument you
will find ghosts (appropriate for Halloween!) of other pieces.

Lynn Yarbrough
369.4HARE::GILBERTThu Oct 31 1985 11:093
Re 369.2:

At fault is the statement: "But no move could accomplish that".
369.5BEING::POSTPISCHILFri Nov 01 1985 09:2612
Re .4:

Are you sure?  At that point, I was discussing a situation in which black
was moving to accomplish the revealed check.  If black had had any other
piece, it would still be on the board.  Therefore, it must have been the
rook, the bishop, or the king that moved.  Obviously, the king could not
have revealed both the rook and the bishop.  And the bishop could not have
moved to where it is and revealed the rook.  Nor could the rook have moved
to where it is and revealed the bishop.  (Is the board drawn correctly?)


				-- edp
369.6SPRITE::OSMANFri Nov 01 1985 09:4911
I can sympathize with edp, as I had the same puzzlement.

I've now seen the answer, and *maybe* I would have eventually thought
of it.  It's really very clever !


			*HINT* follows . . .

Consider some of the less frequent maneuvers employed in chess.

/Eric
369.7BEING::POSTPISCHILFri Nov 01 1985 10:196
Re .6:

Okay, I got it.  Thanks.


				-- edp
369.8AURORA::HALLYBFri Nov 01 1985 12:1752
The following game results in the diagram given in .0 above.  Not exactly
your typical game, but it shows a legal sequence of moves that can lead to
the position.

If you haven't solved the puzzle this will be a spoiler if you continue reading.

  White		  Black

P/Q2-Q4         N/KN1-KB3
N/KN1-KB3       P/QR2-QR4
B/QB1-KN5       N/QN1-QB3
B/KN5xN/KB6     P/K2xB/KB3
N/KB3-K5        N/QB3xN/K4
P/Q4xN/K5       P/KB3xP/K4
P/KB2-KB4       P/K4xP/KB5
N/QN1-QB3       R/QR1-QR3
Q/Q1-Q5         R/QR3-Q3
Q/Q5xR/Q6       B/KB1xQ/Q3
N/QB3-QN5       Q/Q1-KR5
P/KN2-KN3       Q/KR5xP/KN6
P/KR2xQ/KN3     P/KB5xP/KN6
B/KB1-KN2       P/KR2-KR4
R/KR1xP/KR5     R/KR1xR/KR4
N/QN5xB/Q6      P/QB2xN/Q3
O-O-O           P/QR4-QR5
R/Q1xP/Q6       P/KB2-KB3
R/Q6xP/KB6      P/Q2-Q3
R/KB6xP/Q6      P/KN2-KN3
R/Q6xP/KN6      R/KR4-QN4
R/KN6xP/KN3     R/QN4xP/QN7
B/KN2-QB6       K/K1-K2
B/QB6xP/QR4     R/QN7xP/QR7
K/QB1-QN1       R/QR7-QR6
P/K2-K3         R/QR6xP/K6
K/QN1-QR1       R/K6xR/KN6
K/QR1-QR2       K/K2-Q3
K/QR2-QN1       K/Q3-K4
K/QN1-QB1       K/K4-Q5
K/QB1-QN2       B/QB1-K3
K/QN2-QR1       K/Q5-K6
K/QR1-QN2       P/QN2-QN4
K/QN2-QB3       K/K6-K7
K/QB3-QN4       R/KN6-KN5
K/QN4-QR3       B/K3-KB4
K/QR3-QN2       P/QN4-QN5
K/QN2-QN3       B/KB4-K5
K/QN3-QN2       R/KN5-KN4
K/QN2-QR2       R/KN4-QN4
K/QR2-QN2       K/K7-Q8
K/QN2-QN3       B/K5-Q4
P/QB2-QB4       P/QN5xG/QB6ep
K/QN3xP/QB3