# Solve the Puzzle: Find the Odd Coin in 3 Weighings

• Harut82
In summary, there is a well-known coin problem where you have twelve coins, eleven of which are identical and one that is either heavier or lighter. With the help of a balance and only three chances to use it, you must figure out both which coin is the "odd" one and whether it is heavier or lighter. This problem has been posted multiple times and there is a more complex variation available for those seeking a greater challenge.
Harut82
You have twelve coins, eleven identical and one different. You do not know whether the "odd" coin is lighter or heavier than the others. Someone gives you a balance and three chances to use it. The question is: How can you make just three weighings on the balance and find out not only which coin is the "odd" coin, but also whether it's heavier or lighter?

this has been posted here repeatedly. There's a variation to this coin problem that is much more complex, I saw it at "ibm ponder this" a couple of years ago...it makes this problem seem too easy. You can search there "ponder this" database if you want a real challenge.

This is a classic problem in the field of puzzle-solving and mathematical logic. In order to solve this puzzle in three weighings, we need to use a strategy called "divide and conquer". Here is one possible solution:

1. First, divide the twelve coins into three groups of four coins each. Place one group on each side of the balance.

2. If the two sides of the balance are equal, then the odd coin is in the fourth group that was not weighed. If one side is heavier than the other, then the odd coin is in that group.

3. Now, take the group with the odd coin and divide it into two groups of two coins each. Place one group on each side of the balance.

4. If the two sides of the balance are equal, then the odd coin is one of the two coins that were not weighed. If one side is heavier than the other, then the odd coin is in that group.

5. Finally, take the group with the odd coin and weigh the two coins against each other. If one side is heavier, then that is the odd coin. If they balance, then the odd coin is the one that was not weighed.

This strategy works because each weighing provides us with information that helps narrow down the possible locations of the odd coin. By dividing the coins into smaller groups, we are able to eliminate more possibilities with each weighing. This approach can be applied to any number of coins as long as we have three weighings to use.

## 1. What is the puzzle "Find the Odd Coin in 3 Weighings" about?

The puzzle involves a set of coins where one coin is slightly lighter or heavier than the rest. The objective is to use a weighing scale only 3 times to determine which coin is the odd one out.

## 2. How do you approach solving this puzzle?

There are multiple strategies to solve this puzzle, but the most efficient approach is to divide the coins into groups and weigh them against each other. By narrowing down the group with the odd coin, you can continue to divide and weigh until you have identified the odd coin.

## 3. What factors should be considered when solving this puzzle?

The number of coins, the type of weighing scale, and the number of weighings allowed are important factors to consider. Additionally, understanding the concept of balanced and unbalanced weight distributions is crucial to solving the puzzle.

## 4. Is this puzzle solvable every time with only 3 weighings?

Yes, the puzzle is solvable every time with 3 weighings, regardless of the number of coins. However, the strategy and approach may differ depending on the number of coins and the type of weighing scale.

## 5. Are there any real-world applications for this puzzle?

The concept of finding the odd coin in a set using a limited number of weighings can be applied in various fields such as cryptography, computer science, and even in real-life scenarios like finding counterfeit coins. It also helps develop critical thinking and problem-solving skills.

• General Discussion
Replies
10
Views
1K
• General Discussion
Replies
1
Views
3K
• General Discussion
Replies
8
Views
3K
• Set Theory, Logic, Probability, Statistics
Replies
57
Views
3K
• General Discussion
Replies
4
Views
2K
• General Discussion
Replies
9
Views
5K
• General Discussion
Replies
28
Views
20K
• Precalculus Mathematics Homework Help
Replies
4
Views
3K
• General Discussion
Replies
7
Views
3K
• General Math
Replies
10
Views
3K