05 Feb '11 21:43>
If on a chess board each square could be black or white - how many combinations of boards could there be?
Originally posted by greenpawn34so the guy will give you a dollar for every point?
18,446,744,073,709,551,615 grains of rice weighing 461,168,602,000 tons. (thank you Wiki).
Now this is Swiss Gambit territory.
At the start of a game using the beginner formula.
Queen = 9
Rook = 5
Bishop = 3
Knight = 3
Pawn = 1
After winning a bet the loser askes you to contruct a game saying he wiil
give you £1.00 in value for every ...[text shortened]... how many possible pawn promotions (thus making £1 = £9)
can you squeeze out of a game of chess?
Originally posted by dogfish44That's exactly what I mean-
No, because if you do EVERY single combination facing 1 way, the others oon the other sides are already done.
2^64 is correct.
Originally posted by greenpawn34Reveal Hidden Content
18,446,744,073,709,551,615 grains of rice weighing 461,168,602,000 tons. (thank you Wiki).
Now this is Swiss Gambit territory.
At the start of a game using the beginner formula.
Queen = 9
Rook = 5
Bishop = 3
Knight = 3
Pawn = 1
After winning a bet the loser askes you to contruct a game saying he wiil
give you £1.00 in value for every ...[text shortened]... how many possible pawn promotions (thus making £1 = £9)
can you squeeze out of a game of chess?
Originally posted by ua41To solve the problem when rotation of the board is allowed but flipping (i.e. mirror images) are not:
That's exactly what I mean-
so you'd have some redundant combinations because they are just "flipped" images of each other so 2^64 is too many.
Just think of one the corner squares as black, the rest as white. This accounts for 4 different sets, flip it 90 degrees and you'll end up with a different corner as black. This one coloring scheme accounts for 4 combinations
Originally posted by Arctic PenguinMy God, why must everything be over-analyzed and complicated?? Do you flip the board or rotate it when you play chess? NO. Then just solve the problem as if it was a chessboard glued to the table in front of you. Jeeeez.
[quote]Originally posted by ua41
[b]That's exactly what I mean-
so you'd have some redundant combinations because they are just "flipped" images of each other so 2^64 is too many.
Just think of one the corner squares as black, the rest as white. This accounts for 4 different sets, flip it 90 degrees and you'll end up with a different corne ...[text shortened]... he 10th digit.
This method seems sound to me, but I might have miscounted somewhere.
Originally posted by Bebop5Most chess boards I've seen don't specify which end is for black and which end is for white, so yes it probably does get rotated between games. The puzzle is a bit too simple if the board is just fixed to the table, don't you think?
My God, why must everything be over-analyzed and complicated?? Do you flip the board or rotate it when you play chess? NO. Then just solve the problem as if it was a chessboard glued to the table in front of you. Jeeeez.