On a chess board, in how many different ways can 6 consecutive squares be chosen on the diagonals along a straight path ?
- (a) 4
- (b) 6 ✓ UPSC's answer
- (c) 8
- (d) 12
Why the answer is (b)
• The official answer (b) takes 'the diagonals' to mean the two main diagonals of the chessboard, each running corner to corner through 8 squares.
• On a line of 8 squares, a run of 6 consecutive squares can start at square 1, 2 or 3 — 3 ways.
• Two main diagonals give 3 + 3 = 6 ways — option (b).
• (If every diagonal line of the board were counted, the lines of length 7 and 6 would add 6 more ways each side, giving 18, which is not among the options.)
Why the other options are wrong
- (a) 4
- Each main diagonal gives 3 ways, so the two give 6, not 4.
- (c) 8
- Two main diagonals of 8 squares give 3 + 3 = 6 ways, not 8.
- (d) 12
- Two main diagonals of 8 squares give 3 + 3 = 6 ways, not 12.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2021, held on 10 October 2021. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.