Newsgroups: rec.puzzles
From: hoey@aic.nrl.navy.mil (Dan Hoey)
Date: 05 Oct 1994 16:13:48 GMT
Subject: Re: 8 bishops puzzle from "The 7th Guest"

mum...@Aztec.co.ZA (Michael Rolfe) posted the puzzle: four black
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
Hoey@AIC.NRL.Navy.Mil