The counterfeit coin problem, also known as the 10 coins weight puzzle, is a well-known logic puzzle that requires finding a single fake coin among 10 coins that all look identical. This puzzle is frequently used during interviews to evaluate a candidate’s ability to solve problems and apply logical reasoning skills.

So, You have 10 identical-looking coins, and one of them is fake. You know that the fake coin weighs either more or less than the other coins, but you do not know which. You also have a balance scale, and you can use it only three times to determine which coin is fake and whether it weighs more or less than the other coins.

## 10 coins weight puzzle **solution**

Here’s one possible solution:

- Divide the coins into three groups of three coins each, and keep one group of four coins aside.
- Weigh two of the groups of three coins against each other using the balance scale.
- If the two groups of three coins balance each other, then the fake coin must be in the group of four coins that were kept aside. Weigh two of the coins from this group against each other to determine which one is fake and whether it weighs more or less than the other coins.
- If the two groups of three coins do not balance each other, then the fake coin must be in one of the two groups that were weighed. Take the group that weighs less and weigh two of the coins against each other. If they balance each other, then the fake coin must be the remaining coin in that group, which weighs less. If they do not balance each other, then the fake coin must be one of the two coins that were weighed, and you can determine whether it weighs more or less than the other coins based on the results of the weighing.

Hi Rohit,

Let’s say I have 9 coins that weigh 1 unit, and 1 coin that weighs 2 units.

They are broken into groups of the following weights: [2,1,1], [1,1,1], [1,1,1,1]

I take the groups of three, select the lighter group, and match any two of the coins.

It’s not true that if these two coins are equal, the third in the group must be the counterfeit and lighter.

-Mark

Hi Rohit,

There is a similar problems with 25 race-horse that might interest you and your readers.

https://mindyourdecisions.com/blog/2017/05/11/can-you-solve-the-25-horses-puzzle-google-interview-question/