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Old September 18th 05, 05:12 PM
gamo
 
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Default How many horses?


How many horses could stand without menacing each other
in a chess board?











s




p




o




i




l




e




r





I think they were 32, but not for sure.
Cheers,




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Old September 19th 05, 03:28 AM
gamo
 
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On Mon, 18 Sep 2005, CeeBee wrote:

How many horses could stand without menacing each other
in a chess board?


With one horse on the chessboard it's pretty crowded already, even a smaller
one. I guess you mean "knights"?

LOL
Touche. I was meaning "knights"


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Old September 20th 05, 04:13 AM
 
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Yes, the answer is 32, and the reason is very simple. When a knight is
on a particular square, what color squares is it threatening
(menacing)?

jm

p.s. This is one of the puzzles in the Majestic Chess Adventure, btw.

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Old September 20th 05, 09:44 AM
David Richerby
 
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wrote:
Yes, the answer is 32, and the reason is very simple. When a knight is
on a particular square, what color squares is it threatening
(menacing)?


That's not enough to prove it. All that shows is that, with a knight on
every white square, you can't add any extra knights. It also tells you
that, if you remove one knight from that position, you can't put it back
anywhere else. Your argument doesn't address the possibility of coming up
with a completely different position with knights on both black and white
squares where there are more than 32 on the board. In other words, you've
shown that this solution is, in some sense, locally optimal but not shown
that it's globally optimal.

The answer is 32, though.


Dave.

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Old September 20th 05, 08:32 PM
 
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My solution was very much in the spirit of chess. In particular, when a
GM says "this position is drawn -- anybody can see that", and "anybody"
means "anybody who can see the board as well as I do". :-)

I wasn't concerned about giving a proof, but merely the most obvious
answer.

jm



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