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?
Explanation:
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 (∵ 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).
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