The peaceful bishops

mathsyperson · 2007-02-07 01:47:31

I read about this problem ages ago, but just now stumbled upon it again and remembered how frustrating it was to try and solve. I still haven't managed it yet.

On a 5x4 chessboard, there are 4 white bishops on the 1st row and 4 black bishops on the 5th row. The challenge is to get all the bishops to switch places, but in a way so that no bishop is ever under attack by another one of the opposite colour.
(For non-Chess players, bishops can move diagonally as far as they want in one move, but without moving past another piece)

I don't see why it couldn't be done, but I also don't see how to do it. Very well done to anyone who manages to either find a set of moves or prove there isn't one.

Jai Ganesh · 2007-02-12 16:11:57

I shall try this one on a piece of paper, and tell you how far I could go!

mathsyperson · 2007-02-13 03:47:34

1) That relies on me being able to do the necessary coding, which I can't.

2) Would that even work? I wouldn't have thought it possible to brute force, because one possible sequence of moves would be (1, 2, 1, 2, 1, 2, 1, 2...), where '1' moves some bishop to some square, and then '2' moves it back to its starting position.
Because it's possible to get trapped in loops like that, I wouldn't have thought that a computer program would be very effective at this. I may be wrong, of course.

justlookingforthemoment · 2007-02-13 20:56:59

What I got on the first go:

.BW.
BW..
....
WB..
.WB.

I'm pretty much as stuck as everyone else.

espeon · 2007-02-17 07:04:03

how about... just swapping them and cheating.... it always works...

Math Is Fun Forum

#1 2007-02-07 01:47:31

The peaceful bishops

#2 2007-02-12 16:11:57

Re: The peaceful bishops

#3 2007-02-13 03:47:34

Re: The peaceful bishops

#4 2007-02-13 20:56:59

Re: The peaceful bishops

#5 2007-02-17 07:04:03

Re: The peaceful bishops

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