On a chess board, in how many different ways can 6 consecutive squares be chosen on the diagonals along a…
On a chess board, in how many different ways can 6 consecutive squares be chosen on the diagonals along a straight path?
4
6
8
12
Solution
On an 8 × 8 chess board the two main diagonals each have 8 squares. On a line of 8 squares, 6 consecutive squares can be chosen in $8 - 6 + 1 = 3$ ways. With two such diagonals, the total number of ways = $3 + 3 = 6$.