Use your logical skills to solve this riddle.
You have 12 balls that look identical in shape, color etc. All of them have same weight except one ball which is defective. You don’t know whether the defective one is heavier or lighter than other balls. You can use a two sided balance system (not the electronic one). The minimum number of measures required to separate the defective ball is three. Find the way in which you can separate the defective ball.
Answer and explanation to the defective Ball Puzzle:
Divide the balls into 3 groups of 4 balls each.
1. First weigh :
Weigh any 2 groups, one on each side.
There will be two cases.
A. The weight on both side is equal i.e. these two groups don’t have the defective ball.
You know 8 balls are of equal weight and one of the remaining 4 balls have a defective one. Name these four as B1, B2, B3, B4.
B. One side has less weight than the other side.
2. Second weigh :
Case A:
Take B1 & B2 and weigh them.
i. If they are unequal then either B1 is defective or B2. Compare B1 with one of eight balls. If B1 is equal to that then B2 is defective otherwise B1.
Total measurements in this case: 1 (first weigh)+1 (second weigh)+1 (B1 with other ball) = 3
ii. If B1 and B2 are equal then either B3 is defective or B4. Compare B3 with one of eight balls. If B3 is equal to that then B4 is defective otherwise B3.
Total measurements in this case: 1 (first weigh)+1 (second weigh)+1 (B3 with other ball) = 3
Case B:
Mark the balls in the side with less weight as L and with more weight as M. We get 4L and 4M.
Second weigh:
Take 2L and 1M in One side say A and take 2L and 1M in Other side say B of balance system. 1M and 1L are reserved for now.
i. If side A is down and next side goes up then it has two possibilities.
a. One of 2L in A has less weight than other 7 balls
b. The 1M in B has more weight
ii. If side B is down then it also has two possibilities.
a. One of 2L in A has less weight than other 7 balls.
b. One of 1M in B has more weight than other 7 balls
iii. Both sides are balanced
Third weigh :
In cases (i) or (ii) we will get 3 balls (2L and 1M) after the second weigh.
For case (i) and (ii)of (b) :
Weigh two L balls with each other, if they are equal then the 1M is heavier and if they are not then the ball with less weight is defective.
For case (iii) of (b) :
In this case one of the two reserved balls is defective. We have 2M balls. Weigh them, the one which is heavier is defectives.
separate 4 balls , then further divide the other 8 into groups of 4 n 4 , put the new groups on the balance ,the heavier side’s 4 balls can be selected if balance shows unequal weight .However if balance shows equal weight , the separated group of 4 can be selected .In either of the case group of 4 balls will be left .divide them into groups of 2-2 then further into 1-1 and find the defective ball