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There are 6561 balls out of them 1 is heavy. Find the min. no. of times the balls have to be weighed for finding out the heavy ball.
Correct answer is '8'. Can you explain this answer?
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There are 6561 balls out of them 1 is heavy. Find the min. no. of time...
**Finding the Heavy Ball: 8 Weighings**
To find the heavy ball out of 6561 balls, we can use a balanced scale to compare groups of balls against each other. By dividing the balls into smaller groups and comparing their weights, we can narrow down the search for the heavy ball.
**Dividing the Balls**
First, we need to divide the 6561 balls into smaller groups to weigh them. We will divide them into 3 groups, each containing 2187 balls.
**First Weighing: Group A vs. Group B**
Weigh Group A (2187 balls) against Group B (2187 balls) on the scale.
- If the scale is balanced, it means the heavy ball is not in Group A or Group B. Proceed to the next steps.
- If the scale is unbalanced, it means the heavy ball is in either Group A or Group B. Proceed to the next steps.
**Second Weighing: Group A vs. Group B**
Divide Group A and Group B into 3 smaller groups each, containing 729 balls.
Weigh Group A1 (729 balls) against Group B1 (729 balls) on the scale.
- If the scale is balanced, it means the heavy ball is not in Group A1 or Group B1. Proceed to the next steps.
- If the scale is unbalanced, it means the heavy ball is in either Group A1 or Group B1. Proceed to the next steps.
**Third Weighing: Group A1 vs. Group B1**
Divide Group A1 and Group B1 into 3 smaller groups each, containing 243 balls.
Weigh Group A11 (243 balls) against Group B11 (243 balls) on the scale.
- If the scale is balanced, it means the heavy ball is not in Group A11 or Group B11. Proceed to the next steps.
- If the scale is unbalanced, it means the heavy ball is in either Group A11 or Group B11. Proceed to the next steps.
**Fourth Weighing: Group A11 vs. Group B11**
Divide Group A11 and Group B11 into 3 smaller groups each, containing 81 balls.
Weigh Group A111 (81 balls) against Group B111 (81 balls) on the scale.
- If the scale is balanced, it means the heavy ball is not in Group A111 or Group B111. Proceed to the next steps.
- If the scale is unbalanced, it means the heavy ball is in either Group A111 or Group B111. Proceed to the next steps.
**Fifth Weighing: Group A111 vs. Group B111**
Divide Group A111 and Group B111 into 3 smaller groups each, containing 27 balls.
Weigh Group A1111 (27 balls) against Group B1111 (27 balls) on the scale.
- If the scale is balanced, it means the heavy ball is not in Group A1111 or Group B1111. Proceed to the next steps.
- If the scale is unbalanced, it means the heavy ball is in either Group A1111 or Group B1111. Proceed to the next steps.
**Sixth Weighing: Group A1111 vs. Group B1111**
Divide Group A1111 and Group B1111 into 3 smaller groups each, containing 9 balls.
To find the heavy ball out of 6561 balls, we can use a balanced scale to compare groups of balls against each other. By dividing the balls into smaller groups and comparing their weights, we can narrow down the search for the heavy ball.
**Dividing the Balls**
First, we need to divide the 6561 balls into smaller groups to weigh them. We will divide them into 3 groups, each containing 2187 balls.
**First Weighing: Group A vs. Group B**
Weigh Group A (2187 balls) against Group B (2187 balls) on the scale.
- If the scale is balanced, it means the heavy ball is not in Group A or Group B. Proceed to the next steps.
- If the scale is unbalanced, it means the heavy ball is in either Group A or Group B. Proceed to the next steps.
**Second Weighing: Group A vs. Group B**
Divide Group A and Group B into 3 smaller groups each, containing 729 balls.
Weigh Group A1 (729 balls) against Group B1 (729 balls) on the scale.
- If the scale is balanced, it means the heavy ball is not in Group A1 or Group B1. Proceed to the next steps.
- If the scale is unbalanced, it means the heavy ball is in either Group A1 or Group B1. Proceed to the next steps.
**Third Weighing: Group A1 vs. Group B1**
Divide Group A1 and Group B1 into 3 smaller groups each, containing 243 balls.
Weigh Group A11 (243 balls) against Group B11 (243 balls) on the scale.
- If the scale is balanced, it means the heavy ball is not in Group A11 or Group B11. Proceed to the next steps.
- If the scale is unbalanced, it means the heavy ball is in either Group A11 or Group B11. Proceed to the next steps.
**Fourth Weighing: Group A11 vs. Group B11**
Divide Group A11 and Group B11 into 3 smaller groups each, containing 81 balls.
Weigh Group A111 (81 balls) against Group B111 (81 balls) on the scale.
- If the scale is balanced, it means the heavy ball is not in Group A111 or Group B111. Proceed to the next steps.
- If the scale is unbalanced, it means the heavy ball is in either Group A111 or Group B111. Proceed to the next steps.
**Fifth Weighing: Group A111 vs. Group B111**
Divide Group A111 and Group B111 into 3 smaller groups each, containing 27 balls.
Weigh Group A1111 (27 balls) against Group B1111 (27 balls) on the scale.
- If the scale is balanced, it means the heavy ball is not in Group A1111 or Group B1111. Proceed to the next steps.
- If the scale is unbalanced, it means the heavy ball is in either Group A1111 or Group B1111. Proceed to the next steps.
**Sixth Weighing: Group A1111 vs. Group B1111**
Divide Group A1111 and Group B1111 into 3 smaller groups each, containing 9 balls.
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There are 6561 balls out of them 1 is heavy. Find the min. no. of times the balls have to be weighed for finding out the heavy ball.Correct answer is '8'. Can you explain this answer?
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