CAT 2017 Slot 2 — DILR Question 24
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.
Suppose the queen is the only piece on the board and it is at position d5.
In how many positons can another piece be placed on the board such that it is safe from attack from the queen?
Answer & solution
- A
32
- B
35
36
- D
37
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Let Q represent the position of the queen at cell D5. Now none of the pieces can be along column D or along row 5 i.e., a total of 8 + 8 – 1 = 15 cells (âµ D5 is common to column D and row 5 it is counted twice, hence we subtract 1) Now cells along the diagonal of D5 have to be eliminated since they can be directly attacked by the Queen from that cell. Therefore cells A8, B7, C6, E4, F3, G2, H1 and G8, F7, E6, C4, B3, A2 i.e., a total of 13 cells are not to be considered. So a total of 64 – 28 = 36 positions are considered safe from attack if the queen is at position D5
Hence, option (c).