8 bishops puzzle from "The 7th Guest"
Michael Rolfe
the puzzles. It involves a 5-rank, 4-file chessboard with four white
bishops facing four black bishops (all bishops are on their own back
rank to start with).
They make the conventional chess bishop move except they are not allowed
to move into a position where they might be taken. This is VERY limiting.
The object is to move each of the 8 bishops from his back rank to his
opponents' back rank, i.e. the end position is the same as the start
position excep with colours switched.
I have spent too long on this and got nowhere. Can anyone else help?
--
--[ Mike Rolfe in The Cape of Good Hope ]
[ mum...@aztec.co.za in "The fair ^[ in all the world" ]
Goran Wicklund
> I have been playing "The 7th Guest" and have been beaten by one of
> the puzzles. It involves a 5-rank, 4-file chessboard with four white
> bishops facing four black bishops (all bishops are on their own back
> rank to start with).
>
> They make the conventional chess bishop move except they are not allowed
> to move into a position where they might be taken. This is VERY limiting.
>
> The object is to move each of the 8 bishops from his back rank to his
> opponents' back rank, i.e. the end position is the same as the start
> position excep with colours switched.
>
> I have spent too long on this and got nowhere. Can anyone else help?
>
assumed not!
The board can be divided into two distinct part, black and white squares
(as on a chess board). A bishop on a black square can never take a
bishop on a white square. In my solution below, I have only considered
two+two bishops on black squares. For the complete solution, the moves
have to be repeated for the the other bishops.
Label the rows 1-5 and the columns A-D. At start, the bishops are at
positions A1,C1,A5 and C5.
The moves (one move can include change of direction).
C1-B2
C4-B4-D2
B2-D4-C5
A1-B2-A3
A5-C3-A1
D2-C3
A3-C1
C5-A3
C3-D4
C1-D2-A5
A3-B4
D4-B2-C1
B4-C4
Done!
I have not tried to look for solutions with fewer moves.
Goran Wicklund
Dan Hoey
bishops at one end of a 4 x 5 chessboard must exchange places with
four white bishops at the other end, with neither side exposed to
capture.
eua...@eua.ericsson.se (Goran Wicklund) writes:
> You do not say if the moves have to be white-black-white etc. I have
> assumed not!
That assumption is unnecessary. Take any non-alternating solution for
the bishops on white squares. There is an isomorphic solution for the
bishops on the black squares with the colors of the bishops reversed.
In each two moves, take one move of the white-square solution and one
move of the black-square solution. Because the colors of the bishops
involved in those two moves are different, alternating order can be
chosen.
Michael Rolfe mentioned that 18 moves on each square-color is
necessary and sufficient; my program agrees.
Dan Hoey
Ho...@AIC.NRL.Navy.Mil
don preston
: In article q...@ticsa.com, mum...@Aztec.co.ZA (Michael Rolfe) writes:
: > I have been playing "The 7th Guest" and have been beaten by one of
: > the puzzles. It involves a 5-rank, 4-file chessboard with four white
: > bishops facing four black bishops (all bishops are on their own back
: > rank to start with).
: >
: > They make the conventional chess bishop move except they are not allowed
: > to move into a position where they might be taken. This is VERY limiting.
: >
: > The object is to move each of the 8 bishops from his back rank to his
: > opponents' back rank, i.e. the end position is the same as the start
: > position excep with colours switched.
: >
: > I have spent too long on this and got nowhere. Can anyone else help?
: >
:
The key to solving the bishops puzzle (without cheating) is to ignore one of the colors alltogether. Since they are on different colored squares,
If you can do white, you can do black.
Wei-Hwa Huang
>I have been playing "The 7th Guest" and have been beaten by one of
>the puzzles. It involves a 5-rank, 4-file chessboard with four white
>bishops facing four black bishops (all bishops are on their own back
>rank to start with).
>I have spent too long on this and got nowhere. Can anyone else help?
I solved the game and others will pose the solution, so I just
wanted to mention the source.
This problem, to the best of my knowledge, was created by H.E.Dudeney
and was printed in his "Amusement in Mathematics." In there
he gave a complete solution. (Actually, he started with a puzzle with
10 spaces and 2 counters of each color, then showed how it might
apply to the bishops puzzle.) I believe Sam Loyd also took the puzzle
as his own.
Aren't you happy to know that you're having headaches over a puzzle that
was solved completely 100 years ago? :)
-- Wei-Hwa