Question

a simple 9 ball puzzle , one ball is light in weight . in how many minimum balance you can find out this light weighted ball.

Answer 1

I think this can be achieved in 2 steps.

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 right - Group1 has a light ball.Weighing scale tilts on left - Group2 has a light ball.Weighing scale remains balanced -  Group3 has a light 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 light ball.Weighing scale tilts on right - B8 is the light ball.Weighing scale remains balanced - B9 is the light ball.