PR 4 # 13

Wacky · 2006-06-13, 10:26

A castle and a bishop are placed at random on different squares of a chessboard. What is the probability that one piece threatens the other?

Chris Card · 2006-06-13, 11:29

13/36 ?

Chris

fetofs · 2006-06-13, 12:22

259/263? No, it's too high...

Uncwilly · 2006-06-13, 13:21

Zero, castles aren't chess pieces, rooks are.

mfgoode · 2006-06-13, 18:19

Quote:

Originally Posted by Uncwilly

Zero, castles aren't chess pieces, rooks are.

In India both terms are used. So on with the game!
Mally

P.S. Killing time for the Brazil/Croatia match to kick off

retina · 2006-06-14, 04:26

91/256

Fusion_power · 2006-06-14, 04:36

The probability that the rook threatens the bishop is 14/64. This is true no matter where you place the rook or the bishop.

The probability that the bishop threatens the rook depends on position. If the rook is in a corner, the bishop can only threaten from 7 positions. If the rook is on a center square, there are 13 possible positions for the bishop to threaten the rook. I'll leave it to others to figure out what the intervening numbers are and how to treat the set of probabilities.

I make it 24/64 probability that one piece threatens the other.

Chris Card · 2006-06-14, 08:58

Quote:

Originally Posted by Fusion_power

The probability that the rook threatens the bishop is 14/64. This is true no matter where you place the rook or the bishop.

Are you sure? I make it 14/63

retina · 2006-06-14, 12:33

Quote:

Are you sure? I make it 14/63

Oops, I forgot that the two pieces are not allowed to occupy the same square. I change my answer to 91/252

Fusion_power · 2006-06-14, 13:31

You are correct, I should have reduced to 63 since both pieces cannot occupy the same position. Revise the final answer to 24/63.

Wacky · 2006-06-14, 16:43

Some good tries. But I think that Chris got it right on the first shot.

2006-06-13, 10:26	#1
Wacky Jun 2003 The Texas Hill Country 10001000001₂ Posts	PR 4 # 13 A castle and a bishop are placed at random on different squares of a chessboard. What is the probability that one piece threatens the other?

2006-06-13, 11:29	#2
Chris Card Aug 2004 2×5×13 Posts	13/36 ? Chris Last fiddled with by Wacky on 2006-06-13 at 12:15

2006-06-14, 04:36	#7
Fusion_power Aug 2003 Snicker, AL 7×137 Posts	The probability that the rook threatens the bishop is 14/64. This is true no matter where you place the rook or the bishop. The probability that the bishop threatens the rook depends on position. If the rook is in a corner, the bishop can only threaten from 7 positions. If the rook is on a center square, there are 13 possible positions for the bishop to threaten the rook. I'll leave it to others to figure out what the intervening numbers are and how to treat the set of probabilities. I make it 24/64 probability that one piece threatens the other. Last fiddled with by Fusion_power on 2006-06-14 at 04:37

2006-06-13, 12:22	#3
fetofs Aug 2005 Brazil 2·181 Posts	259/263? No, it's too high...

2006-06-13, 13:21	#4
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 2·7·19·37 Posts	Zero, castles aren't chess pieces, rooks are.

2006-06-14, 04:26	#6
retina Undefined "The unspeakable one" Jun 2006 My evil lair 2·11·283 Posts	91/256

2006-06-14, 13:31	#10
Fusion_power Aug 2003 Snicker, AL 7×137 Posts	You are correct, I should have reduced to 63 since both pieces cannot occupy the same position. Revise the final answer to 24/63.

2006-06-14, 16:43	#11
Wacky Jun 2003 The Texas Hill Country 2101₈ Posts	Some good tries. But I think that Chris got it right on the first shot.