Author: José de Jesús García Ruvalcaba
Date: 10:17:12 10/13/98
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On October 13, 1998 at 13:04:17, Ernst A. Heinz wrote: >On October 13, 1998 at 12:23:29, John Coffey wrote: >> >>How many possible positions are there in all 4 or 5 piece endgames? >>I am thinking that it must be between billions and trillions. >>do such endgames take advantage of symetry? > >If you do not discount illegal positions there are 64^X possible constellations >of X pieces. By removing symmetries, not placing more than one piece on the same >square, and not placing the Kings directly beside each other, you can easily >reduce this number to: > > (a) 462 * 62 * 61 for 4-piece endgames without Pawns, > (b) 3612 * 24 * 62 for 4-piece endgames with a single Pawn, > (c) 3612 * 24 * 47 for 4-piece endgames with 2 Pawns (no en-passant), > > (d) 462 * 62 * 61 * 60 for 5-piece endgames without Pawns, > (e) 3612 * 24 * 62 * 61 for 5-piece endgames with a single Pawn, > (f) 3612 * 24 * 47 * 62 for 5-piece endgames with 2 Pawns (no en-passant), > (g) 3612 * 24 * 47 * 46 for 5-piece endgames with 3 Pawns (no en-passant). > >I have submitted an article to the ICCA Journal which describes the according >index schemes among other things. > >=Ernst= That gives a grand total of 1167385380 (please check, I could have mistyped). How many more position are added by taking in account en-passant?
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