If there are 100 bags and each of them is containing 100 coins one of the bag is of artificial coins the weight of each artificial coinis 9gram and the weight of each real coin is 10gm find whichbagis?

Answer 1

Presumably, your question is to find the fewest number of measurements you would need to determine which bag holds the fakes if all you had was a balance scale. The answer is 5, although it may require only 4 depending on which bag is actually found to be fake. 1. Put 33 bags on each side. If one side is lighter, that group of 33 contains the fakes; if they are equal, you know that the fakes are in one of the remaining 34 bags. (I shall refer to the group containing the bag of fakes as the "suspect group.") 2. Put 11 of the suspect group on each side of the balance. If one side is lighter, that group of 11 contains the fake; if they are equal, you know that the fake is one of the remaining 12. 3. Put 4 of the suspect group on each side of the balance. If one side is lighter, that group of 4 contains the fake; if they are equal, you know that the fake is one of the remaining 3. 4. Put 1 of the suspect group on each side of the balance. If one side is lighter, that bag contains the fakes; if they are equal, you know that the fakes are in one of the two bags left unweighed (or is the unweighed bag if the suspect group in step 3 above had only 3 bags. 5. If there are still two bags left, put one on each side of the scale - the lighter one contains the fakes.