To find the counterfeit coin, which is lighter than the rest, using the balance scale, we can follow the below approach:

1. Divide the 9 coins into three groups of 3 coins each: Group A, Group B, and Group C.

2. Compare Group A and Group B on the balance scale:

   • If they balance, then the fake coin is in Group C.
   • If they do not balance, then the fake coin is either in Group A or Group B.

3. Take the group that contains the fake coin (either Group A or Group B) and divide it into three individual coins (Group D, Group E, and Group F).

4. Compare Group D and Group E on the balance scale:

   • If they balance, then the fake coin is in Group F.
   • If they do not balance, then the fake coin is either in Group D or Group E.

5. Take the group that contains the fake coin (either Group D or Group E) and compare two individual coins from that group (let's say Group G and Group H) on the balance scale.

   • If they balance, then the fake coin is the remaining coin in that group.
   • If they do not balance, then the lighter coin is the fake coin.

By following this approach, we can determine the counterfeit coin with a minimum of 2 weighings.

Now, let's go through each option to understand why it is correct or incorrect:

Option A) 3 - This option is incorrect because we can determine the counterfeit coin with a minimum of 2 weighings, as explained above.

Option B) 2 - This option is correct because we can determine the counterfeit coin with a minimum of 2 weighings, as explained above.

Option C) 4 - This option is incorrect because we can determine the counterfeit coin with a minimum of 2 weighings, as explained above.

Option D) 6 - This option is incorrect because we can determine the counterfeit coin with a minimum of 2 weighings, as explained above.

The correct answer is B) 2. This option is correct because we can determine the counterfeit coin with a minimum of 2 weighings, as explained above.

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• Wrong explanation