UPSC Prelims 2005 Q121: Science & Technology – Quantitative Aptitude

UPSC Prelims 2005, General Studies Paper I · Science & Technology

There are 10 identical coins and each one of them has ‘H’ engraved on one face and ‘T’ engraved on the other face. These 10 coins are lying on a table and each one of them has the ‘H’ face as the upper face. In one attempt, exactly four (neither more nor less) coins can be turned upside down. What is the minimum number of attempts in which the ‘T’ faces of all the 10 coins can be brought to be the upper faces?

(a) 4
(b) 7
(c) 8
(d) Not possible

Answer: (a) 4

Explanation

> Note for students: The true minimum is 3 attempts, which is not among the printed options (4, 7, 8, Not possible). The published key is (a) 4, the nearest option. Choose (a) or skip it to avoid a negative mark.

Turning ten coins with four flips at a time

Step	Result
Flips needed	Each coin must be turned an odd number of times, so at least 10 flips
Flips available	4 per attempt, so 2 attempts give only 8 flips and 3 attempts give 12
Plan for 3 attempts	Attempt 1: coin X and coins 1-3; attempt 2: coin X and coins 4-6; attempt 3: coin X and coins 7-9
Result	Coin X is turned 3 times and the other nine once each, so all ten show T

Two attempts give only 8 flips, fewer than the 10 needed, so at least three are required, and the plan above achieves it in exactly 3 attempts. The printed options are 4, 7, 8 and 'Not possible', so the true minimum is not among them; option (a) 4 is the nearest and is the published key.

Answer: (a) 4 (nearest option and published key; the true minimum is 3).

Why each option is right or wrong

(a) CORRECT. 4 attempts also work and is the nearest option, but the true minimum is 3.
(b) Incorrect. 7 attempts are far more than needed.
(c) Incorrect. 8 attempts are far more than needed.
(d) Incorrect. The task is possible, as the plan above shows.

Key point

Parity: every coin must be turned an odd number of times; count flips and divide by 4.

Remember

Ten coins can all be turned to T in 3 attempts of four flips each.

Common mistakes

Rounding up to 4 attempts without testing a 3-attempt plan.
Thinking the number of attempts must be a multiple of 5 coins.
Declaring the whole task impossible by parity.

Exam tip

Count total flips needed and divide by flips per attempt, then check parity.

Sources

Arun Sharma — How to Prepare for Logical Reasoning for the CAT (puzzles and parity arguments)
R. S. Aggarwal — A Modern Approach to Verbal and Non-Verbal Reasoning (Puzzle Test)

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