CAT 2017 Slot 2 — DILR Question 22
Answer the following question based on the information given below.
In an 8 × 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 given by the combination of column and row labels. For example, position c5 means that the piece is cth column and 5th row.
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?
Answer & solution
- A
f8
- B
a7
- C
c1
d3
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Let P1, P2, P3, P4, P5 and P6 be the 6 pieces at positions A1, A3, B4, D7, H7 and H8 respectively.
1] If the queen is at position F8 it can attack P6 as it is in the same row and P3 as it in a diagonal position. However it cannot attack P2, which is in a diagonal position as P3 is placed between P2 and Q along the same diagonal. So a total of 2 pieces can be attacked if the queen is at position F8.
2] If the queen is at position A7 it can directly attack P4 as it is in the same row and P2 as it is in the same column. However it cannot attack P5 because P4 is in between the queen and P5. Similarly it cannot attack P1 because P2 is in between the Queen and P1. So a total of 2 pieces can be attacked by the queen if it is at position A7.
3] If the queen is at position C1, then it can only attack P1 which is in the same row and P2 which is along the same diagonal as the queen. So at positions C1, the queen can attack only 2 pieces.
4] If the queen is at position D3 then it can attack P2 along the same row, P4 along the same column and P5 along the same diagonal i.e., a total of 3 pieces. So out of the given options, the queen at position D3 can attack maximum number of pieces.
Hence, option (d).