You have 8 identical-looking coins. One of these coins is counterfeit and is known to be lighter than the others. You also have a two-pan balance scale. How can you identify the fake coin by using the scale only twice?
Split the coins into 3 groups – 2 groups with 3 coins each and 1 group with 2 coins.
Now put the 2 groups of 3 coins on the scale.
Scenario #1: Both groups weigh the same. This means that the counterfeit coin is in the group with 2 coins. So take the 2 coins from that group and use the scale to determine the counterfeit coin.
Scenario #2: One group weighs less than the other. Take any 2 coins from this group of 3 coins. If they weigh the same, then the 3rd coin is the counterfeit coin. If they don’t weigh the same, then the lighter one is obviously the counterfeit coin.