Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #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.

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.

Offline

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

ganesh
Administrator
Registered: 2005-06-28
Posts: 25,317

### Re: The peaceful bishops

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

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

Offline

## #3 2007-02-13 03:11:23

kylekatarn
Member
Registered: 2005-07-24
Posts: 445

### Re: The peaceful bishops

well, if you are really desperate you can always try solving by brute-force

Last edited by kylekatarn (2007-02-13 03:51:11)

Offline

## #4 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.

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.

Offline

## #5 2007-02-13 03:55:31

kylekatarn
Member
Registered: 2005-07-24
Posts: 445

### Re: The peaceful bishops

there are ways to get around that problems, with graphs or lists of moves for example. But I have to agree with you, puzzle algorithms are not very direct and simple.

Offline

## #6 2007-02-13 04:14:46

kylekatarn
Member
Registered: 2005-07-24
Posts: 445

### Re: The peaceful bishops

I was able to reach this config

``````.BB.
B..B
.....
W..W
.WW.``````

but seems a deadlock

Last edited by kylekatarn (2007-02-13 04:15:21)

Offline

## #7 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.

Offline

## #8 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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Offline

## Board footer

Powered by FluxBB