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1.  You have a weighing machine, and you have 27 balls in which 26 balls are of same weight and 1 ball is of different weight. How many times/steps needed to identify the 1 ball which is different from other ball?

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### Replies to This Discussion

There are two scenerios

1-Divide balls in 3 groups of 9. then weight them if weight are equals then those are perfact balls keep aside them.Now take 6 ball from remaining 9 balls and 6 from normal balls and weight them if new balls weight is up or low then you will find that deffective ball is lighter or heavier(here we consider heavier is deffective).if that will equals then weight 3 remaining balls with three normal balls..if new balls weight is up or low then you will find that deffective ball is lighter or heavier(heavier is deffective as we assume.then put one- one ball in both weight if they are equal then deffective ball is in your hand..if weight is low/up then you can find deffective ball...i suggest you when you read it draw it on paper then you can understand easily...

2-if in first two 9-9 balls if weight is heavier/lighter then measure it with remaining 9 balls if both 9-9 balls are equals then deffective one ball is  in first 9 balls . then do same premaining process..

I hope you can understand it.....

minimum 3 steps to maximum 26 steps....

Hi Omprakash,

May I know what kind of weighing machine is used?

1. 2 plateform  - where only 1 ball can be put at a time
2. Single plateform/Hanging/electronic - where only 1 ball can be put at a time

For case1, max number of steps would be 13 & for case2 it will be 26 max.

This can have a lot of answers, just thing with all sorting methodologies like bubble, heap etc.

Thanks,

Javed Nihal Jamali

we have to solve it  in minimum steps.here we use any type of weighing machine.

Hi omprakash,

the question seem to me from probability

same weight balls are =26

different weight balls are =1

we can use the empirical formula of probability

P(E)=no of different weight balls/total no of weight balls

=1/27

=0.037

Regard's

lakshmi kanth reddy

Hi laxmi what about weighing machine which have given u to find out???????

make groups of 27 balls in 9,9,9.

Comapre 2 groups.

Make groups of 9 (which contain defected ball) into 3,3,3

Comapre 2 groups.

Compre 2 balls from 3(which contain defected ball)

if these 2 are not of same weight then compare one of them with remaining

Now you definitely find out the defected ball......

27 = 9 + 9 + 9
step 1 divide in three equal part and weight two part if both are equal then third one has default ball
if we get default ball part and again divide in three equal part
9 = 3 + 3 + 3
step 2 again do same process step 1
3 = 1 + 1 + 1

step 3 follow the step 1

-> 3 steps

if you don't if the defect ball is lighter or heavier you need to compare all group's of 9 balls. one group will be heavier or lighter than the other 2. this would add one more step in the beginning, thus resulting in:

-> 4steps

Hi Sathya,

Good one.

Step 1:

26/2= 13

Put 13 balls each side.. if they are same weight then remaining 1 ball is the required ball..

if it is not then Step 2:

take 13 balls which are having more weight.

12/2 = 6

Put 6 balls each side.. if they are same weight then remaining 1 ball is the required ball..

if it is not then Step 3:

take 6 balls which are having more weight.

6/2 = 3

Put 3 balls each side..

Step 4:

take 3 balls which are having more weight.

2/2 = 1

Put 1 ball each side.. if they are same weight then remaining 1 ball is the required ball.. else ball which is having more weight is the required ball

So minimum 1 or 2 steps and maximum 4 steps

Hii you all In this case we dont know wether defective ball is lighter or heavier? we have to find defective balls weight first.For that we have to compare all 3 group.