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Minor pieces on a chessboard


Best Answer bonanova, 11 April 2014 - 11:05 AM

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5 replies to this topic

#1 BMAD

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Posted 03 April 2014 - 12:53 PM

Consider a an infinite chessboard.  

 

How many squares can a knight reach after precisely n moves?

How about a bishop?

 

 


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#2 bonanova

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Posted 03 April 2014 - 05:38 PM

Spoiler for Looks like


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#3 BobbyGo

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Posted 04 April 2014 - 03:42 PM

Spoiler for Not a Complete Answer...but

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#4 BMAD

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Posted 04 April 2014 - 07:59 PM

Spoiler for Looks like

 

 

Spoiler for Not a Complete Answer...but

Both are well said but there seems to be disagreement as to the knight moves; however the balancing issue that BobbyGo references may be an issue resolved by Bonanova's equation.


Edited by BMAD, 04 April 2014 - 08:01 PM.

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#5 bonanova

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Posted 10 April 2014 - 08:55 AM

Spoiler for on futher consideration


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#6 bonanova

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Posted 11 April 2014 - 11:05 AM   Best Answer

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




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