You have 6561 balls. 1 is lighter than remaining. What is the minimum number of weighings required on a common balance to ensure that the odd ball is identified ?

(a) 8 (b) 7 (c) 6 (d)5

• For such questions power of 3 is used.
  
  Let there be 3 balls, 1 out of them is heavy, minimum number of weighings to find the heavy ball is = 1
  
  First take any 2 balls, if they are in balance => the 3rd ball is heavy.
  if they are not in balance, we get the heavier ball.
  Thus minimum number of weighings = 1
  
  For 9 such balls, where 1 is heavy , it would be = 2 .
  [ In the 1st weighing 3 balls on each side of balance. if they are in balance, another weighing with remaining 3 balls is required.
  if they are not in balance, the heavier side having 3 balls is weighed again.]
  Thus minimum number of weighings = 2
  
  Similarly for 10-27 balls, minimum number of weighings = 3
  28 - 81 balls, minimum number of weighings = 4
  82 - 243 balls,minimum number of weighings = 5
  244 - 729 balls, minimum number of weighings = 6
  730 - 2187 balls, minimum number of weighings= 7
  2188 - 6561 balls, minimum number of weighings = 8
  
  Therefore, answer would be (a)8.
• 12 years agoHelpfull: Yes(2) No(0)
• 8 weighings are reqd.
  3^8 = 6561
  
• 12 years agoHelpfull: Yes(0) No(2)