There are 10 cig packs each containing an unknown no of cigs( each = Pack has between 50 and 100). One pack has all bad cigs . Each good cig = ( if u can agree that any cig is good) weighs 1gm. Each bad cig weighs = 1.1 gm or .99 gm but all bad cigs weigh same. Using a spring chemical = Balance ( which gives u the exact weight) .find out which pack is bad ,Using the balance only once.

• Mark the packets with numbers 1 to 10.
  Take 1 cig from Pack 1.
  Take 2 cig from pack 2.
  ..
  ..
  Take 10 cig from Pack 10.
  Weigh all 55 cigarettes.
  In normal case weight should be 55 gms.
  Due to faulty cigarettes, weight will be different.
  Depending on weight diff, we can get number of faulty cigarettes and hence faulty pack also.
• 11 years agoHelpfull: Yes(25) No(32)
• Take 1 cig from Pack 1, 2 cig from pack 2, 3 cig from pack 3, 4 cig from pack 4, 5 cig from pack 5, .. .. . 10 cig from pack 10.Then If all are gud..Total weight of cig will be 1 +2 + 3
  + .. .10 = 55 gm
  If Defective is in pack 1.Then sum will be 54.9 or 55.1
  If Defective is in pack 2.Then sum will be 54.8 or 55.2
  If Defective is in pack 3.Then sum will be 54.7 or 55.3
• 10 years agoHelpfull: Yes(15) No(0)
• @noori, with this solution we can come to conclusion that the cigret weight is either 0.99 or 1.1 but we can't come to the solution that which pack contain faulty weight.
• 10 years agoHelpfull: Yes(8) No(0)