you have 6 iron balls. 5 iron balls have equal weight and 1 iron ball is slightly lighter than the other 5 iron balls. you are given a libra. find ways (most minimum) to find out the light.

typically in this type of question, you can only use a "fair balance"

1st weighing:
place 3 balls on each side of the balance, that will tell you which set of 3 contains the lighter ball

2nd weighing:
place a ball on each side of the balance, keep the third back in your hand.
a) If they balance, the the ball in your hand is the lightest
b) If the balls don't balance, it will show which is the lightest.

2 weighings are necessary.

should have said:

2nd weighing:
From the set of balls with the lighter ball, place a ball on each side of the balance, keep the third back in your hand.
etc

To find the light iron ball using a balance scale (libra), you can follow these steps:

Method 1: 3 Weighings (minimum number of weighings)

Step 1:
- Divide the 6 iron balls into two equal groups of 3 balls each.
- Weigh these two groups on the balance scale.

There are three possible outcomes:
1. If the two groups have the same weight, the light iron ball must be in the group of 3 balls that haven't been weighed yet. Proceed to Step 2.
2. If one group is lighter than the other group, the light iron ball must be in the lighter group. Proceed to Step 2.
3. If one group is heavier than the other group, the light iron ball must be outside of these two groups. Proceed to Step 2.

Step 2:
- Take the group of 3 balls identified as potentially containing the light iron ball.
- Choose any two balls from this group and weigh them against each other.

There are two possible outcomes:
1. If the two balls weigh the same, the light iron ball must be the one ball that hasn't been weighed yet. It is the lighter ball. Proceed to Step 3.
2. If one ball is lighter, then it is the light iron ball. Proceed to Step 3.

Step 3:
- Take the remaining two balls from the previous step.
- Weigh both of these balls on the balance scale.

There are two possible outcomes:
1. If the two balls weigh the same, then the light iron ball is the one that hasn't been weighed yet, and it is the lighter ball.
2. If one of the balls is lighter, then that is the light iron ball.

Method 2: 2 Weighings

Alternatively, you can find the light iron ball using only two weighings by following these steps:

Step 1:
- Divide the 6 balls into two groups of 3 balls each.
- Weigh these two groups on the balance scale.

There are three possible outcomes:
1. If the two groups have the same weight, the light iron ball must be in the group of 3 balls that haven't been weighed yet. Proceed to Step 2.
2. If one group is lighter than the other group, the light iron ball must be in the lighter group. Proceed to Step 2.
3. If one group is heavier than the other group, the light iron ball must be outside of these two groups. Proceed to Step 2.

Step 2:
- Take the group of 3 balls identified as potentially containing the light iron ball.
- Weigh two out of the three balls against each other.

There are two possible outcomes:
1. If the two balls weigh the same, the light iron ball must be the one ball that hasn't been weighed yet. It is the lighter ball.
2. If one ball is lighter, then it is the light iron ball.

By using either of these methods, you can find the light iron ball using a balance scale with the minimum number of weighings.