IAS 2014 — CSAT Reasoning

2014mcqmedium

Six identical cards are placed on a table. Each card has number ‘1’ marked on one side and number ‘2’ marked on its other side. All the six cards are placed in such a manner that the number ‘1’ is on the upper side. In one try, exactly four (neither more nor less) cards are turned upside down. In how many least number of tries can the cards be turned upside down such that all the six cards show number ‘2’ on the upper side?

Official previous-year question

Verified 2 Aug 2026.

Options

A3
B5
C7
DThis cannot be achieved

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Solution

Correct Option (A)

The problem requires determining the minimum number of tries to change the state of six cards from all '1's to all '2's, by flipping exactly four cards in each try.

Let the initial state of the cards be represented by the sequence of numbers on their upper sides. Initially, all six cards show '1', so the state is 111111.

Try 1: Flip cards 1, 2, 3, and 4.

The state of the cards becomes 222211. (Four cards show '2', two cards show '1').

Try 2: From the state 222211, flip cards 1, 2, 3, and 5.

Card 1 changes from '2' to '1'.
Card 2 changes from '2' to '1'.
Card 3 changes from '2' to '1'.
Card 5 changes from '1' to '2'.
The state of the cards becomes 111221. (Three cards show '1', three cards show '2').

Try 3: From the state 111221, flip cards 1, 2, 3, and 6.

Card 1 changes from '1' to '2'.
Card 2 changes from '1' to '2'.
Card 3 changes from '1' to '2'.
Card 6 changes from '1' to '2'.
The state of the cards becomes 222222. (All six cards show '2').

This sequence demonstrates that the objective can be achieved in 3 tries. It can be further established that fewer than 3 tries are insufficient. After one try, two cards will still show '1'. To convert these two '1's to '2's, at least one more try is needed, which would involve flipping two '1's and two '2's. This operation would result in two '1's and four '2's, meaning the goal is not reached in two tries. Therefore, a minimum of 3 tries is required.

Incorrect Options:

Options (B) 5 and (C) 7: Since the task can be accomplished in 3 tries, 5 or 7 cannot be the least number of tries.
Option (D) This cannot be achieved: The step-by-step demonstration above proves that the objective is achievable within a finite number of tries.

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Correct Option (A)

The problem requires determining the minimum number of tries to change the state of six cards from all '1's to all '2's, by flipping exactly four cards in each try.

Let the initial state of the cards be represented by the sequence of numbers on their upper sides. Initially, all six cards show '1', so the state is 111111.

Try 1: Flip cards 1, 2, 3, and 4.

The state of the cards becomes 222211. (Four cards show '2', two cards show '1').

Try 2: From the state 222211, flip cards 1, 2, 3, and 5.

Card 1 changes from '2' to '1'.
Card 2 changes from '2' to '1'.
Card 3 changes from '2' to '1'.
Card 5 changes from '1' to '2'.
The state of the cards becomes 111221. (Three cards show '1', three cards show '2').

Try 3: From the state 111221, flip cards 1, 2, 3, and 6.

Card 1 changes from '1' to '2'.
Card 2 changes from '1' to '2'.
Card 3 changes from '1' to '2'.
Card 6 changes from '1' to '2'.
The state of the cards becomes 222222. (All six cards show '2').

Incorrect Options:

Options (B) 5 and (C) 7: Since the task can be accomplished in 3 tries, 5 or 7 cannot be the least number of tries.
Option (D) This cannot be achieved: The step-by-step demonstration above proves that the objective is achievable within a finite number of tries.

IAS 2014 — CSAT Reasoning

Options

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Correct Option (A)

Incorrect Options:

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IAS 2014 — CSAT Reasoning

Options

Did you get this right?

Solution

Correct Option (A)

Incorrect Options:

Your note

IAS Reasoning in other years

More IAS Reasoning questions

Other CSAT topics for IAS

Comprehension

Maths

Keep practicing Reasoning