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

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

The peaceful bishops

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. smile

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.


Why did the vector cross the road?
It wanted to be normal.

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

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

Re: The peaceful bishops

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


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: The peaceful bishops

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

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.


Why did the vector cross the road?
It wanted to be normal.

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

justlookingforthemoment
Moderator
Registered: 2005-05-26
Posts: 2,161

Re: The peaceful bishops

What I got on the first go:

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

I'm pretty much as stuck as everyone else.

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

espeon
Real Member
Registered: 2006-02-05
Posts: 2,586

Re: The peaceful bishops

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


Presenting the Prinny dance.
Take this dood! Huh doood!!! HUH DOOOOD!?!? DOOD HUH!!!!!! DOOOOOOOOOOOOOOOOOOOOOOOOOD!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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