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# Ten Boxes

Ten boxes are there. Each ball weighs 100 gms. One ball is weighing 90 gms.
i) If there are 3 balls (n=3) in each box, how many times will it take to find 90 gms ball?
ii) with n=10
iii) with n=9
This question is related to TCS Interview
Asked by: neeti tripathi | Member Since Dec-2009 | Asked on: Dec 16th, 2009
souravray_88

Answered On : Feb 7th, 2010

6 Chances.
First keep 5 boxes in each in a balance. Then the one with low weight. Take it divide 5 boxes as 2-2-1.
Keep 2-2 in each of balance. If both weigh same... then take the one left. In which we have 3 balls.
1-1-1
Keep any 2 balls in balance. If both weigh the same. The one left is of low weight..!
Else if both don't weigh the same then the one with low weight is the one req. as such is for n 10.

aman15490

Answered On : Feb 10th, 2010

It would  Only take 4 Iterations to determine the 90 gm ball( In First Case n=3). Let's have a Look

1. Pair of 5 - 5 boxes. The Box Pair That Goes Down Is The One Pair That Contains The 90 gm ball.

2. Keep 1 Box aside.

Now Make pair of 2 - 2 boxes.If Both Lie On the Same Position Then It is the other box

Remember: In such questions You are required to find the worst possible case.

So again, the Box Pair That Goes Down Is The One That Contains The 90 gm ball.

3. Now We Are Only Having 2 Boxes.Now again put them in Balance.

The Box That Goes Down Is The oneThat Contains The 90 gm ball.

4. Now Take Out The Balls .Put One Of the Balls aside.And Weight Them In Balance.

The One That Goes Down Is Our Ball. Or If Both Equal Then the ball Kept Aside Is The 90 gm Ball.

Similarly We Can Proceed For Other Cases.The Difference Would Occur Only In The 4'th Step that is when We Are Actually Taking The Balls Out Of The Box.

1 User has rated as useful.

Deepak90

Answered On : Sep 20th, 2010

If there are 10 boxes only 3 times weighing is enough

Ist time place 3-3

If one side is less then take one box in hand from that side and weight other 2
as 1-1, if they are equal the box in your hand is less weight

else in 3-3 both are equal means

place remaining 4 as

IInd Time 2-2 separate the lesser sides boxes as

IIIrd Time 1-1 you can find the lesser box

If there are 9 boxes only 2 times weighing is enough

Ist time place 3-3

If one side is less then take one box in hand from that side and weight other 2
as 1-1

IInd Time otherwise repeat the same for the remaining 3 boxes