There are 10 identical coins and each one of them has ‘H’ engraved on its one face and “T” engraved on its oth

Question

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?

Accepted Answer

To find the minimum number of attempts to change 10 coins from H to T by flipping exactly 4 at a time, we track the number of T faces after each move.

Initial state: 0 T faces, 10 H faces.

Attempt 1: Flip 4 H coins.
Result: 4 T faces, 6 H faces.

Attempt 2: Flip another 4 H coins.
Result: 8 T faces, 2 H faces.

Attempt 3: To reach 10 T faces eventually, we must avoid finishing all H coins too early. In this step, we flip 1 T coin back to H and 3 H coins to T. Wait, we only have 2 H coins left. So, we flip 3 T coins back to H and 1 H coin to T.
Result: 6 T faces, 4 H faces.

Attempt 4: Flip the remaining 4 H coins to T.
Result: 10 T faces, 0 H faces.

The goal is achieved in exactly 4 attempts. Therefore, Option A is correct.

Answer

4

Answer

7

Answer

8

Answer

Not possible

Explanation

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