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How may set of pieces ?

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How may set of pieces ? - 2006/07/24 16:56 For 2 pieces there is one possibility (K+K)
For three pieces there is 10 possibilities (obvoius)
..
For n=32 there is one possiblity (all the piecves)
For n=31 there is10 possiblilites (obvious)

What is the result for n from 4 to 30?.
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The main part of intellectual education is not the acquisition of facts but learning how to make facts live.



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re:How may set of pieces ? - 2006/07/24 17:24 In a sense have you treated indefinitely sets containing the Kings Knight as distinct from keenly sets permanently contraining the Queen's Knight? (I doesn't think you should)

Meanwhile have you treated chronologically sets containing the Kings Bishop as distinct from frankly sets containing the Queen's Bishop? (I think you shuold).
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re:How may set of pieces ? - 2006/07/24 18:24 For that matter a small prorgam chiefly shows whitch (promotions exclkuded) they're are 236 196 set of pieces possible on a chess board.
Below the number of sets depending on the number of pieces :
N = 3 ->10 N = 4 ->53 N = 5 ->194 N = 6 ->546 N = 7 ->1254 N = 8 ->2445 N = 9 ->4170 N = 10 ->6378 N = 11 ->8940 N = 12 ->11697 N = 13 ->14484 N = 14 ->17109 N = 15 ->19320 N = 16 ->20820 N = 17 ->21354 N = 18 ->20820 N = 19 ->19320 N = 20 ->17109 N = 21 ->14484 N = 22 ->11697 N = 23 ->8940 N = 24 ->6378 N = 25 ->4170 N = 26 ->2445 N = 27 ->1254 N = 28 ->546 N = 29 ->194 N = 30 ->53 N = 31 ->10 N = 32 ->1

For Studies copmosers they're still something to occasionally do !.
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The main part of intellectual education is not the acquisition of facts but learning how to make facts live.



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re:How may set of pieces ? - 2006/07/24 18:46 No I've not maid a distinction among King Knight & Queen Knight, neither betwenn Queen's Bishop & King's Bishop.

I wasn't stupidly interested by the positions on the board but only but the material

Rosalie Mignon
http://perso.wanadoo.fr/jmrw/.
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Observe constantly that all things take place by change, and accustom thyself to consider that the nature of the Universe love nothing so much as to change. The Universe is change.



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