9 balls are there one of them is of higher wt and remaining all are of same. given is one weighing scale and you can use it two times. How will you find the heavy ball in two trials only.
Let us give name to each ball as B1, B2, B3, B4, B5, B6, B7, B8, B9.
Now divide all the balls into 3 groups.
Group1 – (B1, B2, B3), Group2 – (B4, B5, B6), Group3 – (B7, B8, B9)
STEP1 – We can weigh any two groups. Let’s assume we choose Group1 on left side of the scale and Group2 on the right side.
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 1. Then Group 1 has a heavy ball.
STEP 2 – Now weigh any two balls from Group1. Lets assume we keep B1 on left side of the scale and B2 on right side.
So now when we weigh these two balls we can get 3 outcomes.
Weighing scale tilts on left – B1 is the heavy ball.
Weighing scale tilts on right – B2 is the heavy ball.
Weighing scale remains balanced – B3 is the heavy ball.
(The same step applies if the group 2 or group3 has the heavy ball)
Balls- B1, B2, B3, B4, B5, B6, B7, B8, B9.
Split into 3 groups.
Group1 – (B1, B2, B3), Group2 – (B4, B5, B6), Group3 – (B7, B8, B9)
Now weigh any two groups. Group1 on left side of the scale and Group2 on the right side.
When weighing scale (tilts left – Group1 has a heavy ball) or (tilts right – Group2 has a heavy ball) or (balanced – Group3 has a heavy ball)
Lets assume it tilts left then Group 1 has a heavy ball.
Now weigh any two balls from Group1. B1 on left side of the scale and B2 on right side.
When weighing scale (tilts left – B1 is the heavy ball) or (tilts right – B2 is the heavy ball) or (balanced – B3 is the heavy ball)
Balls- B1, B2, B3, B4, B5, B6, B7, B8, B9.
Group1 – (B1, B2, B3), Group2 – (B4, B5, B6), Group3 – (B7, B8, B9)
Now weigh any two groups. Group1 on left side of the scale and Group2 on the right side.
When weighing scale tilts left – Group1 has a heavy ball or right – Group2 has a heavy ball or balanced – Group3 has a heavy ball.
Lets assume Group 1 has a heavy ball.
Now weigh any two balls from Group1. B1 on left side of the scale and B2 on right side.
When weighing scale tilts left – B1 is the heavy or tilts right – B2 is the heavy or balanced – B3 is the heavy.
Let us give name to each ball as B1, B2, B3, B4, B5, B6, B7, B8, B9.
Now divide all the balls into 3 groups.
Group1 – (B1, B2, B3), Group2 – (B4, B5, B6), Group3 – (B7, B8, B9)
STEP1 – We can weigh any two groups. Let’s assume we choose Group1 on left side of the scale and Group2 on the right side.
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 1. Then Group 1 has a heavy ball.
STEP 2 – Now weigh any two balls from Group1. Lets assume we keep B1 on left side of the scale and B2 on right side.
So now when we weigh these two balls we can get 3 outcomes.
Weighing scale tilts on left – B1 is the heavy ball.
Weighing scale tilts on right – B2 is the heavy ball.
Weighing scale remains balanced – B3 is the heavy ball.
(The same step applies if the group 2 or group3 has the heavy ball)
Balls- B1, B2, B3, B4, B5, B6, B7, B8, B9.
Split into 3 groups.
Group1 – (B1, B2, B3), Group2 – (B4, B5, B6), Group3 – (B7, B8, B9)
Now weigh any two groups. Group1 on left side of the scale and Group2 on the right side.
When weighing scale (tilts left – Group1 has a heavy ball) or (tilts right – Group2 has a heavy ball) or (balanced – Group3 has a heavy ball)
Lets assume it tilts left then Group 1 has a heavy ball.
Now weigh any two balls from Group1. B1 on left side of the scale and B2 on right side.
When weighing scale (tilts left – B1 is the heavy ball) or (tilts right – B2 is the heavy ball) or (balanced – B3 is the heavy ball)
Balls- B1, B2, B3, B4, B5, B6, B7, B8, B9.
Group1 – (B1, B2, B3), Group2 – (B4, B5, B6), Group3 – (B7, B8, B9)
Now weigh any two groups. Group1 on left side of the scale and Group2 on the right side.
When weighing scale tilts left – Group1 has a heavy ball or right – Group2 has a heavy ball or balanced – Group3 has a heavy ball.
Lets assume Group 1 has a heavy ball.
Now weigh any two balls from Group1. B1 on left side of the scale and B2 on right side.
When weighing scale tilts left – B1 is the heavy or tilts right – B2 is the heavy or balanced – B3 is the heavy.