# You have 8 balls. One of them is defective and weighs less than others. You have a balance to measure balls against each other. In 2 weighings how do you find the defective one?

divide the balls into three groups. Let group A contains 3

balls group B contains 3 balls and group C contains 2 balls.

FIRST TIME: BALANCE the groups A and B.

case 1:

If they are equal then the defective ball is in group C.

case 2: if they are not equal then take the group of 3

balls which has less weight.

SECOND TIME:

IF the defective ball is in group C, we can easily find the

ball which is less.

if the defective ball is in group of 3 which has less

weight, take 2 balls out of this group and find the weight.

if they are equal, then the left out is defective. if not

we can find easily the ball which weigh less.

so we have the following steps:

A (3) B(3) c(2)

|_____________| |

first time / |

unequal equal then c has defective.use

| second time to find out

second time take lessweight group

CASE 1: First we should take six balls divided equally and

then it is placed on the two pans.three on one and three on

other..

if the two pans are balanced then the defective ball is not

in the six..then we should the two and keep them one ball

on each.

CASE2: Again We should take any of the six balls and

divided equally and then it is placed on the two pans.. if

any of the pan weighs less than the other.. We should take

the three balls seperately..Now from that three we should

take any two and placed one on each.. fi both the pan

balances the ball which is left over is the defective.. if

one ball weighes less than the other,while keeping one on

each,then it is the defective one….