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Among 12 identical looking golf balls there is one that is defective in weight. It is either heavier or lighter than the standard one. You have a balance. You can only weigh 3 times to find out which one is defective and whether it is heavier or lighter.
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Answer Posted / amit
Make 4 groups of 3 balls each (G1, G2, G3, G4. Picturing a decision tree structure may help as I explain below.
1st Weighing: Place G1 and G2
If Equal then: defective ball in G3 or G4 (Consequently G1 & G2 contain balls all having the same weight i.e. normal balls or control group)
If Not Equal then: defective ball in G1 or G2 (Consequently G3 & G4 contain balls all having the same weight i.e. normal balls or control group)
Assume 1st Weighing is Equal.
2nd Weighing: Place G3 (test) and G1 (control)on pans
If Equal then: defective ball is in G4
If Not Equal then: defective ball in G3. Now if G3 is heavier (pan goes down) that means the abnormal ball is heavier than all others. If G3 is lighter (pan goes up) then that means the abnormal ball is lighter than all others.
Assume 2nd Weighing is Not Equal and G3 group is heavier.
Now we name the 3 balls in G3 group as G3-1, G3-2, G3-3.
3rd Weighing: Place G3-1 and G3-2 on pans.
If Equal then: The G3-3 is the defective (and heavier ball).
If Not Equal then: Then ball in the pan that goes down (i.e. heavier ball) is the defective one.
So 1st Weighing - Narrowing the test group
2nd Weighing - Determining heavy/light status
3rd Weighing - Determining abnormal ball
At any place above depending upon the outcome (Equal / Not Equal) you will have to change the Group in the next weighing accordingly. (E.g. Assume 2nd Weighing was equal then defective ball in G4 - so 3rd weighing you follow same procedure described above with the G4 balls).
I was stumped when I first came across this. And I found no perfect answers online. But some attempts by others helped me figure out part of the solution. Finally I found the missing part (2nd weighing finding heavy/light is crucial and 3rd Weighing with individual balls).
Since many people may be struggling with this - I thought I should help by posting the solution. Test it and vote up if its right!
Cheers!
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