In a basic game of chess, if there's only two pieces left: a king and a rook. How many ways can a king be safe from the opponent's rook if they are placed in all possible combination?
Details and Assumptions :
Assume there is no opponent's king.
This is a Computer Science problem.
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There are 1 4 places in range of the rook, if the rook is placed in any place, excluding its own place. So the rest is 6 3 − 1 4 = 4 9 . Since there are 6 4 probabilities where the rook was placed, so
6 4 ∗ 4 9 = 3 1 3 6