Question

*What is the probability that two kings placed on a regular 8 x 8 chessboard, will be attacking
each other? (A king can attack any square adjacent to its position vertically, horizontally or
diagonally)​

Answer 1

probability is : 420/ 4032 or 10.45 %

king can occupy corners( 4 positions ) or sides ( 6x4 = 24 positions) or Restvof squares ( 36 positions).

the attack directions for corners is 3 , sides is 5 , rest is 8. opponents king has 3/63 or 5/63 or 8/ 63 chance of positioning himself in neighborhood of Attacking king.

prob =( 4/ 64 x 3/ 63) + ( 24/64 x 5/63 )+ ( 36/64x8/63)

= 12/4028 + 120/ 4028 + 288/4028

= 420/4028