Heavier ball Puzzle

August 4, 2020

Heavier Ball Puzzle

You have 8 balls all of the same size. 7 of them weigh the same, and one of them weighs slightly more. How can you find the ball that is heavier by using a balance and only two weighings?

Solution:

Divide the balls into the following groups: (1,2,3),(4,5,6),(7,8)

Step 1.
Weigh (1,2,3) against (4,5,6)

Two possible outcomes:
The two groups are equally heavy. (Case A)
One of these groups is heavier than the other. (Case B)

Case A
Weigh 7 against 8. Now you have identified the heavier ball in 2 weighing.

Case B
Take the heavier group (assume it to be (1,2,3)), take any two balls and weigh them against each other. Either one of these is heavier else the third ball is.

Detailed Analysis

Divide the balls into the following groups: (1,2,3),(4,5,6),(7,8)

Weigh Group A (1,2,3) against Group B(4,5,6).

Now, there are two possibilities that maybe the both the group weigh equal or both do weigh equal.

Case A: When both the group A & B weigh equal.

If Case A happened then measure between ball 7 against 8, and you will find the result that which ball is heavier.

Now, in Case B, one of the group among A & B weigh more. Than, lets suppose Group A (1, 2, 3) is weigh more.

Now, weigh the balls of Group A against each other one after other, and we will find heavier ball in 2 chance.