How many weighings of a balance scale are needed to find a lighter counterfeit coin among six coins?

To find a lighter counterfeit coin among six coins, you would need a maximum of two weighings on a balance scale. Here's how:

Step 1: Divide the six coins into two groups of three. Weigh these two groups against each other.

• If they balance, then the lighter counterfeit coin is in the remaining group of coins that were not weighed.

• If they do not balance, then the lighter counterfeit coin is in the group that weighed less.

Step 2: Now you have a group of three coins, one of which is the lighter counterfeit. Divide this group into three individual coins. Weigh two of these coins against each other.

• If they balance, then the lighter counterfeit coin is the one that was not weighed.

• If they do not balance, then the lighter counterfeit coin is the one that weighed less.

So, in a maximum of two weighings, you can find the lighter counterfeit coin among six coins.