UPSC Prelims 2021 · CSAT
Question 64: Basic Numeracy
On a chess board, in how many different ways can 6 consecutive squares be chosen on the diagonals along a straight path ?
AnswerUPSC’s answer is (b).
Take the board's two long diagonals, each 8 squares. On one diagonal a run of 6 consecutive squares can start at the 1st, 2nd or 3rd square, which is 3 ways. The other long diagonal gives 3 more, so 3 + 3 = 6. Counting runs on every diagonal of the board would give more, but 6 is the option that fits the two long diagonals. Remember: in a line of 8 squares the number of runs of 6 is 8 − 6 + 1 = 3.
How you could have got this
No shortcut here: in a “how many” question, ruling out options doesn’t help. Every statement has to be judged.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) 4 is too few; each long diagonal alone gives 3 runs.
- (b) Right: 3 runs of six squares on each of the two long diagonals.
- (c) 8 would need 4 runs on each diagonal, but there are only 3.
- (d) 12 would need 6 runs on each diagonal; only 3 exist.
Worth knowing: The question does not say which diagonals; counting every diagonal with six or more squares gives 18, which is not an option, so UPSC's key fits only the board's two long diagonals.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2021, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.