2021 JMPSC Sprint Problems/Problem 4

Problem

A standard chess-board is an 8 by 8 grid of squares. A bishop is placed at square C5 (row 5, column C) and a rook is placed at square E4 (row 4, column E). How many squares can be attacked by both the bishop and rook if they each take one move?

(The bishop can attack any square in the same diagonal as itself, including squares A7, F8, G1, D6, and so on. The rook can attack any square in the same row or column as itself, including squares E5, E8, E4, C4, and so on.)

Solution

Simply look at the board.

Draw the paths in which they can go.

You will see that they will intersect at these squares: D4 B4 E7 E3

Therefore, four squares can be attacked by both the bishop and the rook if they each take one move. -OofPirate