Author: Michael Neish
Date: 02:02:48 01/14/00
Go up one level in this thread
>For doubled White A-Pawns, Black can have Doubled Pawns on files >A to F, and in addition, for files B-G the file to the left or >right of the doubled Pawns can be empty. > >For the case of doubled White A-Pawns, we get > >White Doubled A, Black Doubled A = 1.025e9 >White Doubled A, Black Doubled B, no B-Pawn on A-file = 2.567e9 >White Doubled A, Black Doubled B, no B-Pawn on C-file = 4.101e9 >White Doubled A, Black Doubled C, no B-Pawn on B-file = 2.734e9 >White Doubled A, Black Doubled C, no B-Pawn on D-file = 6.561e9 >White Doubled A, Black Doubled D, no B-Pawn on C-file = 6.561e9 >White Doubled A, Black Doubled D, no B-Pawn on E-file = 6.561e9 >White Doubled A, Black Doubled E, no B-Pawn on D-file = 6.561e9 >White Doubled A, Black Doubled E, no B-Pawn on F-file = 6.561e9 >White Doubled A, Black Doubled F, no B-Pawn on E-file = 6.561e9 >White Doubled A, Black Doubled F, no B-Pawn on G-file = 6.561e9 >White Doubled A, Black Doubled G, no B-Pawn on F-file = 6.561e9 >White Doubled A, Black Doubled G, no B-Pawn on H-file = 6.561e9 >White Doubled A, Black Doubled H, no B-Pawn on G-file = 6.561e9 > >Which comes to 7.5012e10. > This calculation allows Black Pawns to be behind White Pawns on the doubled Pawn files. Maybe I should think before posting. If you don't allow any Black Pawns behind White Pawns, it becomes: File containing W and B doubled Pawns = 15 combinations. File containing one set of doubled Pawns and one Pawn of opposing colour = 20 combinations File containing one set of doubled Pawns and no opposing Pawns = 15 combinations File containing one W and one B undoubled Pawn = 15 combinations File containing only one Pawn = 6 combinations File containing no Pawns = 1 combination Based on this, we get. White Doubled A, Black Doubled A = 15x1x15^6 = 1.709e9 White Doubled A, Black Doubled B, no B Pawn on A-file = 15x15x15^6 = 2.563e9 White Doubled A, Black Doubled B, no B Pawn on C-file = 20x15x6x15^5 = 1.367e9 White Doubled A, Black Doubled C, no B Pawn on B-file = 20x1x20x15^5 = 3.038e8 White Doubled A, Black Doubled C, no B Pawn on D-file = 20x6x20x6x15^4 = 7.29e8 White Doubled A, Black Doubled D, no B Pawn on C-file = 20x6x6x20x15^4 = 7.29e8 White Doubled A, Black Doubled D, no B Pawn on E-file = 20x6x15x20x6x15^3 = 7.29e8 White Doubled A, Black Doubled E, no B Pawn on D-file = 7.29e8 White Doubled A, Black Doubled E, no B Pawn on F-file = 7.29e8 White Doubled A, Black Doubled F, no B Pawn on E-file = 7.29e8 White Doubled A, Black Doubled F, no B Pawn on G-file = 7.29e8 White Doubled A, Black Doubled G, no B Pawn on F-file = 7.29e8 White Doubled A, Black Doubled G, no B Pawn on H-file = 7.29e8 White Doubled A, Black Doubled H, no B Pawn on G-file = 7.29e8 Which comes to 1.213e10. Maybe we should rename this thread "see how many different answers we can get for the same thing". Mike.
This page took 0 seconds to execute
Last modified: Thu, 15 Apr 21 08:11:13 -0700
Current Computer Chess Club Forums at Talkchess. This site by Sean Mintz.