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?

[spoiler]13/36[/spoiler] ?

Chris

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

[spoiler]Zero, castles aren't chess pieces, rooks are.[/spoiler]:razz:

Castles/rooks
 

[QUOTE=Uncwilly][spoiler]Zero, castles aren't chess pieces, rooks are.[/spoiler]:razz:[/QUOTE]
:popcorn:
In India both terms are used. So on with the game!
Mally :coffee:
P.S. Killing time for the Brazil/Croatia match to kick off :grin:

[spoiler]91/256[/spoiler]

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.

[QUOTE=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.
[/QUOTE]
Are you sure? I make it 14/63

[QUOTE]Are you sure? I make it 14/63[/QUOTE]Oops, I forgot that the two pieces are not allowed to occupy the same square. I change my answer to [spoiler]91/252[/spoiler]

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

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