There are 6561 balls out of them 1 is heavy. Find the minimum number of times the balls have to be weighed for finding out the heavy ball.

• 3^8=6561
  Ans is: 8
• 5 years agoHelpfull: Yes(5) No(16)
• Answer: 8
  
  
  Explanation:
  
  
  Suppose there are 9 balls
  
  
  
  Let us give name to each ball B1 B2 B3 B4 B5 B6 B7 B8 B9
  
  
  
  Now we will divide all the balls into 3 groups.
  
  
  
  Group1 - B1 B2 B3
  
  
  
  Group2 - B4 B5 B6
  
  
  
  Group3 - B7 B8 B9
  
  
  
  Step1 - Now weigh any two groups. Let's assume we choose Group1 on left side of the scale and Group2 on the right side.
  
  
  
  So now when we weigh these two groups we can get 3 outcomes.
  
  
  
  Weighing scale tilts on left - Group1 has a heavy ball.
  Weighing scale tilts on right - Group2 has a heavy ball.
  Weighing scale remains balanced - Group3 has a heavy ball.
  Lets assume we got the outcome as 3. i.e Group 3 has a heavy ball.
  
  
  
  Step2 - Now weigh any two balls from Group3. Lets assume we keep B7 on left side of the scale and B8 on right side.
  
  
  
  So now when we weigh these two balls we can get 3 outcomes.
  
  
  
  Weighing scale tilts on left - B7 is the heavy ball.
  Weighing scale tilts on right - B8 is the heavy ball.
  Weighing scale remains balanced - B9 is the heavy ball.
  The conclusion we get from this Problem is that each time weigh. We element 2/3 of the balls.
  
  
  
  As we came to conclusion that Group3 has the heavy ball from Step1, we remove 6 balls from the equation i.e (2/3) of 9.
  
  
  
  Simillarly we do the ame thing for the Step2.
  
  
  
  Now going with this conclusion. We have 6561 balls.
  
  
  
  Step - 1
  
  
  
  Divided into 3 groups
  
  
  
  Group1 - 2187Balls
  
  
  
  Group2 - 2187Balls
  
  
  
  Group3 - 2187Balls
  
  
  
  Taking the similar steps as we did in the above example, we come to the conclusion that Group1 has the heavy ball.
  
  
  
  Step - 2
  
  
  
  Divided into 3 groups
  
  
  
  Group1 - 729Balls
  
  
  
  Group2 - 729Balls
  
  
  
  Group3 - 729Balls
  
  
  
  Taking the similar steps as we did in the above example, we come to the conclusion that Group1 has the heavy ball.
  
  
  
  Step - 3
  
  
  
  Divided into 3 groups
  
  
  
  Group1 - 243Balls
  
  
  
  Group2 - 243Balls
  
  
  
  Group3 - 243Balls
  
  
  
  Taking the similar steps as we did in the above example, we come to the conclusion that Group1 has the heavy ball.
  
  
  
  Step - 4
  
  
  
  Divided into 3 groups
  
  
  
  Group1 - 81Balls
  
  
  
  Group2 - 81Balls
  
  
  
  Group3 - 81Balls
  
  
  
  Taking the similar steps as we did in the above example, we come to the conclusion that Group1 has the heavy ball.
  
  
  
  Step - 5
  
  
  
  Divided into 3 groups
  
  
  
  Group1 - 27Balls
  
  
  
  Group2 - 27Balls
  
  
  
  Group3 - 27Balls
  
  
  
  Taking the similar steps as we did in the above example, we come to the conclusion that Group1 has the heavy ball.
  
  
  
  Step - 6
  
  
  
  Divided into 3 groups
  
  
  
  Group1 - 9Balls
  
  
  
  Group2 - 9Balls
  
  
  
  Group3 - 9Balls
  
  
  
  Taking the similar steps as we did in the above example, we come to the conclusion that Group1 has the heavy ball.
  
  
  
  Step - 7
  
  
  
  Divided into 3 groups
  
  
  
  Group1 - 3Balls
  
  
  
  Group2 - 3Balls
  
  
  
  Group3 - 3Balls
  
  
  
  Taking the similar steps as we did in the above example, we come to the conclusion that Group1 has the heavy ball.
  
  
  
  Step - 8
  
  
  
  So now when we weigh 2 balls out of 3 we can get 3 outcomes.
  
  
  
  Weighing scale tilts on left - left side placed is the heavy ball.
  Weighing scale tilts on right - right side placed is the heavy ball.
  Weighing scale remains balanced - remaining ball is the heavy ball.
  So the general answer to this question is, it is always multiple of 3 steps.
  
  
  
  For 9 balls 3² = 9. therefore 2 steps
  
  
  
  For 6561 balls 3^8 = 6561 therefore 8 steps
• 3 years agoHelpfull: Yes(1) No(0)