8 Balls Weight Puzzle (Solved) 8 Balls Weight Puzzle (Solved)

This is my favorite weight puzzle which have been asked from me in many interviews over the past few years.

Puzzle

You have 8 balls identical in size and appearance. One of them is defective and weighs heavy than the others. You have a weighing scale with no measurements so you can just compare weight of balls against each other. How would you find the defective ball in 2 weightings?

Solution

First of all we will give a number to each ball i.e. 1, 2, 3, 4, 5, 6, 7, and 8

The trick to solve these kind of weight problem is to divide them in groups. We will divide these 8 balls in 3 groups:

GroupBall Numbers
group 11, 2, 3
group 24, 5, 6
group 37, 8

Now we keep the group 3 aside and put group 1 balls on one side of scale and group 2 balls on another side of scale [1] with three possible outcomes:-

1. Scale is balanced

That means each ball in group 1 and group 2 are identical in weight and defective one is from group 3.

Let’s put group 3 balls 7 and 8 on each side of scale[2] with two possible outcomes:-

  1. If 7 is heavy then it is defective one
  2. If 8 is heavy then it is defective one

2. group 1 is heavier then group 2

That means defective balls is from group 1 i.e. either 1 or 2 or 3.

Let’s keep number 3 aside and put balls 1 and 2 on each side of scale[2] with three possible outcomes:-

  1. If 1 and 2 balances, then 3 is defective one
  2. If 1 is heavy then it is defective one
  3. If 2 is heavy then it is defective one

3. group 2 is heavier then group 1

That means defective balls is from group 2 i.e. either 4 or 5 or 6.

Let’s keep number 6 aside and put balls 4 and 5 on each side of scale[2] with three possible outcomes:-

  1. If 4 and 5 balances, then 6 is defective one
  2. If 4 is heavy then it is defective one
  3. If 5 is heavy then it is defective one

Reference:-
[1] is weighting for the first time
[2] is weighting for the second time

Conclusion

That’s it guys. We have found the defective balls out of 8 balls in only 2 weightings.

If by now you understood the trick of dividing balls in group and keeping some balls aside then you can solve weight puzzle with any number of balls. Here is the cheat sheet:-

Cheat Sheet
N Balls Weight PuzzleGroupsMin Weightings (Best Case)Min Weightings (Worst Case)
N = 2[1] [2]11
N = 3[1] [2] [3]11
N = 4[1] [2] [3,4]12
N = 5[1,2] [3,4] [5]12
N = 6[1,2] [3,4] [5,6]22
N = 6[1,2,3] [4,5,6] [7]12
N = 8[1,2,3] [4,5,6] [7,8]22
N = 9[1,2,3] [4,5,6] [7,8,9]22
N = 10[1,2,3,4] [5,6,7,8] [9,10]23
N = 11[1,2,3,4] [5,6,7,8] [9,10,11]23
N = 12[1,2,3,4] [5,6,7,8] [9,10,11,12]33

If you are interested in how to solve 12 balls weight puzzle with a twist that you don’t know whether it is light or heavy then check out this post - How to solve 12 balls weight puzzle