# How to Determine Counterfeit Coins with Only One Weighing

• AlexChandler
In summary, there are seven stacks of coins, each consisting of 100 coins. The real coins weigh 10 grams and the counterfeit coins weigh 11 grams. You have an analytical scale accurate to .1 gram and want to determine the fewest number of weighings needed to identify which stacks are counterfeit and how many there are, without knowing if any of the stacks are counterfeit. The answer is 1 weighing, and there is no catch.
AlexChandler
There are seven stacks of coins, each consisting of 100 coins.
You know that real coins weigh 10 grams, but counterfeit coins weigh 11 grams.
You have an analytical scale that is accurate to .1 gram.
Each stack consists of either all real coins or all counterfeit coins, none of the stacks are mixed.
You do not know how many stacks are counterfeit or even if any of them are.
You want to determine how many stacks are counterfeit (if any), and precisely which ones are.
You want to do this in the least possible amount of weighings.

Whats the fewest number of weighings you need to make?
And how do you do it?

Is there a catch? I make it 1.

Take 1, 2, 4, 8, 16, 32, 64 from each pile, measure the excess weight and convert it to a binary number

Jonathan Scott said:
Is there a catch? I make it 1.

Take 1, 2, 4, 8, 16, 32, 64 from each pile, measure the excess weight and convert it to a binary number

I'm impressed. That was fast!

## 1. What are counterfeit coins?

Counterfeit coins are fake or fraudulent copies of real coins that are made with the intention of deceiving people into thinking they are genuine. They are often made with cheaper materials and do not have the same value or quality as real coins.

## 2. How can I spot a counterfeit coin?

There are several ways to spot a counterfeit coin. Look for inconsistencies in the design, such as misspellings or incorrect dates. Also, check the weight and size of the coin as counterfeit coins may differ from the real ones. Lastly, pay attention to the sound the coin makes when dropped on a hard surface. Real coins have a distinct sound, while counterfeit coins may sound dull or fake.

## 3. What are some consequences of using or possessing counterfeit coins?

Using or possessing counterfeit coins is illegal and can result in serious consequences. Depending on the severity of the crime, one could face fines, imprisonment, or both. Additionally, if the counterfeit coins were used to deceive others, one could also face charges of fraud or forgery.

## 4. Can I sell a counterfeit coin?

No, it is illegal to sell counterfeit coins. Doing so would be considered fraud and could result in legal consequences. It is important to always verify the authenticity of your coins before attempting to sell them.

## 5. How can I avoid purchasing counterfeit coins?

To avoid purchasing counterfeit coins, it is important to only buy from reputable dealers or sources. Do your research and educate yourself on the characteristics of genuine coins. It is also helpful to purchase coins that come with a certificate of authenticity from a trusted third-party grading service.

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