In an 8 X 8 chessboard a queen placed anywhere can attack another piece if the piece is present in the same row, or in the same column or in any diagonal position in any possible 4 directions, provided there is no other piece in between in the path from the queen to that piece.
The columns are labelled a to h (left to right) and the rows are numbered 1 to 8 (bottom to top). The position of a piece is given by the combination of column and row labels. For example, position c5 means that the piece is in cth column and 5th row.
1. If the queen is at c5, and the other pieces at positions c2, g1, g3, g5 and a3, how many are under attack by the queen? There are no other pieces on the board.
2. If the other pieces are only at positions a1, a3, b4, d7, h7 and h8, then which of the following positions of the queen results in the maximum number of pieces being under attack?
3. If the other pieces are only at positions a1, a3, b4, d7, h7 and h8, then from how many positions the queen cannot attack any of the pieces?
4. Suppose the queen is the only piece on the board and it is at position d5. In how many positions can another piece be placed on the board such that it is safe from attack from the queen?
1. Queen is at C5. Pieces which are under attack are A3, C2, G1, G5. So, a total of 4 pieces are under attack.
2. Pieces are at A1, A3, B4, D7, H7 and H8.
Option (1): If Queen is at F8, it will attack H8 and B4. A total of 2 pieces.
Option (2): If Queen is at A7, it will attack A3 and D7. A total of 2 pieces.
Option (3): If Queen is at C1, it will attack A1 and A3. A total of 2 pieces.
Option (4): If Queen is at D3, it will attack A3, D7 and H7. A total of 3 pieces.
So, Queen at D3 implies 3 pieces will be under attack (which is the maximum).
3. Queen cannot be placed in Columns - A, B, D, and H. From the remaining columns, it has to be assessed.
For example, Column C: If Queen is placed in C2, it will attack H7. Further, other positions in the column C can be ruled out. Similarly, analyzing other squares, the result is as follows: Queen can be placed in E2, F2, G2, G5 (such that the pieces on board are not under attack). So, there are a total of 4 such squares for the Queen.
4. Given that Queen is at d5. A total of 36 such squares are safe.