You have nine balls, three of which are slightly heavier, and three of which are slightly lighter than the normal three. All three balls in each group has the same weight. All nine balls are identical otherwise. Your mission is to determine the group of every ball using a pair of scales.

How many weighings are needed in order to ensure the accomplishment of your mission?

• It should be 8 as maximum and 4 as minimum.
  
  4 because say the 9 weight are a1 a2 a3, b1 b2 b3 & c1 c2 c3 such that a>b>c and you luckily weighed a1 c1, a2 c2 & a3 c3 then you are sure you have found the three groups as the difference in weights are the same for all the three cases IF a b c are not in AP.
  
  The fourth weighting will be to find the relative position of the two groups of weights found with the third group.
• 12 years agoHelpfull: Yes(2) No(3)
• @ chaitanya,
  
  Can you explain the logic for worst possible case in 8 weighings ?
  
  You are taking chance that u r lucky enough to get result in first case as per your expectation.
  But qn here is to find min chances for each possible case say worst case.
• 12 years agoHelpfull: Yes(0) No(0)