Author: Shep
Date: 04:05:30 01/27/00
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On January 27, 2000 at 03:43:50, Shep wrote: >On January 26, 2000 at 15:07:41, J. Wesley Cleveland wrote: > > >> >>You are doing an extra capture here. e.g. d4 c5 d5 nc6 dc6 and now both the >>white pawn at c6 and the black d pawn can queen. I believe (but have not tried) >>that with 8 captures you can have all 16 pawns promote. > >Of course you can, just as I outlined above. My apologies, I didn't read your post with the required amount of attention. :) You are right. So once more (I hope it's finally right this time): Let's first assume that no pawn captures another pawn (since that would not change the number of additional BNRQ). It suffices if 8 additional captures are made in the way you described it. Without loss of generality, we can assume 4 white pawns and 4 black pawns advance by capturing. Since each side has 2+2+1=5 pieces that can be captured (i.e. if we're talking about promoting to Bishop, there are 2N+2R+1Q), this is possible without reducing the number of pieces to find max() for. Consequently, all 16 pawns can promote without a hitch, yielding max |B| = max |N| = max |R| = 20 max |Q| = 18 q.e.d. --- Shep
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