There are 10 identical coins and each one of them has H engraved on its one face and T engraved on its other face. These 10 coins are lying on a table and each one of them has H face as the upper face. In one attempt, exactly four (neither more nor less)

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Submitted by examrobotsa on

Q: 6 (IAS/2005)
There are 10 identical coins and each one of them has ‘H’ engraved on its one face and “T” engraved on its other face. These 10 coins are lying on a table and each one of them has ‘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 total number of attempts in which the “T” faces of all the 10 coins can be brought to be the upper faces ?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,4,5,4,2,1,2

keywords: 

{'identical coins': [0, 0, 1, 1], 'coins': [2, 0, 1, 1], 'minimum total number': [0, 0, 1, 1], 'upper faces': [0, 0, 1, 0], 'faces': [0, 0, 1, 0], 'upper face': [0, 0, 1, 1], 'attempts': [0, 0, 1, 1], 'other face': [0, 0, 1, 0], 'attempt': [0, 0, 1, 1], 'face': [0, 0, 7, 2], 'table': [0, 0, 1, 0]}

The question asks for the minimum attempts it would take to turn all 10 coins showing "H" to "T" with the rule that exactly 4 coins must be flipped at once.

Option 1 suggests that it would take 4 attempts. Although logically this could be seen as one attempt per four coins, this would only change 8 coins to show "T", leaving 2 coins still showing "H".

Option 2 suggests it would take 7 attempts. This doesn`t align with the rule of flipping exactly 4 coins at once as it would imply flipping less than 4 coins in some attempts.

Option 3, suggesting 8 attempts, suffers from the same issue as option 2, where more attempts have been made than divisible by 4.

Option 4 claims it is not possible to flip all coins to "T".

Alert - the correct answer should be Option 4, `Not possible`. Based on the given conditions, it`s impossible to have all the coins show “T”, since any attempt will always leave an even number of `H` coins, making the goal unattainable.