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MatPlus.Net Forum Promenade A big construction challenge for nightrider experts
 
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(1) Posted by Siegfried Hornecker [Monday, Sep 26, 2011 11:19]; edited by Siegfried Hornecker [11-09-26]

A big construction challenge for nightrider experts


I'd like to see a problem where a nightrider checkmates in all 12 possible ways.

According to an article by Gerson Berlinger (http://b3rn0ull1.blogspot.com/2011/05/think-big.html):
 QUOTE 
Dawson points out that the absolute maximum of 12 mates by a nightrider can be achieved on a board not less than 101 by 121. Any takers?


Same question by me:
Is anyone able to compose this with the smallest possible board size (of course, this could be bigger than 101 by 121, nobody knows)? No fairy pieces or conditions allowed, other than nightriders and the board size.
No prizes here, just for fun and curiosity. :-)

Thanks to Zalmen Kornin for pointing me to that blog!
 
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(2) Posted by Jacques Rotenberg [Monday, Sep 26, 2011 12:38]; edited by Jacques Rotenberg [11-09-26]

Jean-Marc Loustau already did something like that and even more.
 
 
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(3) Posted by Hauke Reddmann [Thursday, Sep 29, 2011 12:01]; edited by Hauke Reddmann [11-09-29]

Mind to post it? Would save me a lot of arcustangents :-)

Hauke

EDIT: I arcustangented anyway, since I love math :-)
My result for a pq-rider:
Min size=t*p*q*(p^2+q^2)^2+1,t*Max[2*p^2*q^2*(p^2+q^2),p2*(p^4-q^4)]+1
(t=2 for even-odd, t=1 for odd-odd)
The result agrees with Dawson for p=2,q=1.
 
 
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MatPlus.Net Forum Promenade A big construction challenge for nightrider experts