Out of 9 equal weight one is faculty find the least number of weighing required to identify a faulty weight using a two pan balance

To identify the faulty weight from 9 equal weights using a two-pan balance, we can apply a strategy similar to a "divide and conquer" method, where the weights are split into groups for comparison.

### Strategy:

1. **First weighing**: Divide the 9 weights into three groups of 3 (Group A, Group B, and Group C). Weigh Group A against Group B.
   - If they balance, the faulty weight is in Group C.
   - If they don't balance, the faulty weight is in the heavier or lighter group.

2. **Second weighing**: Now, take the group identified from the first weighing (whether Group A, B, or C) and divide it into three individual weights. Weigh two of the weights against each other.
   - If they balance, the third weight is the faulty one.
   - If they don’t balance, the heavier or lighter one is the faulty weight.

### Minimum Number of Weighings:
- **First weighing**: Reduces the problem from 9 weights to 3.
- **Second weighing**: Identifies the faulty weight out of 3.

Thus, **2 weighings** are the minimum required to find the faulty weight.

### Summary:
The least number of weighings required to identify the faulty weight out of 9 is **2**.

Would you like further details or examples?

Here are some related questions:
1. How does this strategy change with a different number of weights?
2. What if the balance can only detect heavier, not lighter, objects?
3. Can we identify the faulty weight with more weighings in a different way?
4. What is the reasoning behind dividing the weights into groups of 3?
5. How does this method scale for larger numbers, like 27 or 81 weights?

**Tip:** When using a balance, dividing the problem into smaller chunks often simplifies the solution process.

Out of 9 equal weights, one is faulty. Find the least number of weighings required to identify the faulty weight using a two-pan balance.

Learn how to identify the faulty weight among 9 equal weights using a two-pan balance with a minimum of 2 weighings. This problem illustrates the divide and conquer strategy and logical reasoning, making it suitable for students in Grades 7-10.

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