# How Can You Identify the Counterfeit Coin Among 12 Using Only Three Weighings?

• kant
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kant
You have 12 coins. one of the coin is a counterfeit of some unkown weight. The rest of the coins have identical weight. Use three tries in a pan balance to identify the counterfeit.

First, I would divide the 12 coins into three groups of four coins each. I would then place two groups on each side of the pan balance, leaving the third group aside. If the two groups balance out, then the counterfeit is not in those two groups. If one side is heavier, then the counterfeit is in that group of four coins.

Next, I would take the group of four coins that contains the counterfeit and divide it into two groups of two coins each. I would again place one group on each side of the pan balance. If the two groups balance out, then the counterfeit is one of the two remaining coins. If one side is heavier, then the counterfeit is in that group of two coins.

Finally, I would take the group of two coins that contains the counterfeit and place one coin on each side of the pan balance. If the two coins balance out, then the remaining coin is the counterfeit. If one side is heavier, then that coin is the counterfeit.

By dividing the coins into smaller groups and using the pan balance to compare weights, we can narrow down the possible counterfeit coin to just one in three tries. This method is efficient and reliable in identifying the counterfeit coin among the 12 coins.

## 1. How do you determine which coin is counterfeit?

The most common method to determine which coin is counterfeit is by using a balance scale. Separate the coins into two groups of six and weigh them against each other. The group that is lighter contains the counterfeit coin. If the scale remains balanced, then the counterfeit coin is among the remaining three coins. Repeat the process until the counterfeit coin is identified.

## 2. How many weighings are needed to find the counterfeit coin?

In the worst-case scenario, it will take three weighings to find the counterfeit coin. The first weighing will separate the coins into two groups of six, the second weighing will narrow it down to three coins, and the final weighing will identify the counterfeit coin. However, in some cases, it may be possible to find the counterfeit coin in two weighings.

## 3. Is there a way to identify the counterfeit coin with only one weighing?

No, it is not possible to identify the counterfeit coin with only one weighing. In order to determine the counterfeit coin, it is necessary to compare the weight of the coins against each other in multiple weighings.

## 4. Can the counterfeit coin be heavier or lighter than the genuine coins?

Yes, the counterfeit coin can be either heavier or lighter than the genuine coins. The method of using a balance scale to compare weights can identify a counterfeit coin regardless of whether it is heavier or lighter than the genuine coins.

## 5. Is there a different method to find the counterfeit coin?

Yes, there are other methods to find the counterfeit coin, such as using a coin sorter or analyzing the dimensions and features of the coins. However, the most common and efficient method is using a balance scale to compare weights.

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