Coin Puzzle 2

July 31, 2020

Coin Puzzle 2

A man has 10 bags full of coins. Each bag contains 1000 coins. But one bag is full of forgeries, and he just can’t recall which one. He does know that genuine coins weigh 1 gram, but forgeries weigh 1.1 grams. To hide the fact that he can’t recall which bag contains forgeries, he needs your help.
How can he identify the bag with the forgeries with just one weighing?
A man has 10 bags full of coins. Each bag contains 1000 coins. But one bag is full of forgeries, and he just can’t recall which one. He does know that genuine coins weigh 1 gram, but forgeries weigh 1.1 grams. To hide the fact that he can’t recall which bag contains forgeries, he needs your help. How can he identify the bag with the forgeries with just one weighing?

Solution:

Step 1:

Information provided:

  • Total No. of Bags = 10
  • No.  of Coins in each bag: 1000
  • No. of bag contain forgery Coins: 1 Bag(Unknown)
  • Weight of 1 original Coin: 1 gram
  • Weight of forgery coin: 1.1 grams
  No. of Coins in each bag          
           B1 = 1000
           B2 = 1000
           B3 = 1000
           .
           .
           .
           .
           B10 = 1000

 
Step 2:

It is given that there is only One bag with forgeries.

He can find the bag with Forgery Coins by:

Take 1 one coin from Bag 1, 2 coins from Bag 2, 3 coins from Bag 3 and so on till 10 coins from Bag 10.

  No. of Coins taken from each bag          
           B1 = 1
           B2 = 2
           B3 = 3
           .
           .
           .
           .
           B10 = 10

 

A man has 10 bags full of coins. Each bag contains 1000 coins. But one bag is full of forgeries, and he just can’t recall which one. He does know that genuine coins weigh 1 gram, but forgeries weigh 1.1 grams. To hide the fact that he can’t recall which bag contains forgeries, he needs your help. How can he identify the bag with the forgeries with just one weighing?
 
Step 3:

 

Now weigh all the coins collected from each bag.
i.e.,
Coins from Bag 1 + Coins from Bag 2 + Coins from Bag 3 +……+ Coins from Bag 10
 
If there is no forgeries, then the total weight of all the coins should be:
1 + 2 + 3 + 4 +……+ 10 = 55 grams (As weight of 1 original coin is 1 gram)

Now if the total weight comes out to be 55.3 then it is clear that the 3rd bag contains the forgerier Coins because then the weight added will be 3.3 grams instead of 3 grams.
 
Similarly,  if the total weight comes out to be 55.5 grams then 5th bag contains the forgery coins.
 
So, if the total weight is (55.n), then it is clear that the nth bag contain forgeries.
 
  Total weight of original Coins          
           B1 = 1 gram
         +
           B2 = 2 gram
         +
           B3 = 3 gram
           .
           .
           .
         + 
           B10 = 10 gram
         Total = 55 gram

 

 

Total weight of Coins when forgery 
Coins are included and let say bag 
3 has forgery coins, then 
          
           B1 = 1 gram
         +
           B2 = 2 gram
         +
           B3 = 3.3 gram
           .
           .
           .
         + 
           B10 = 10 gram
         Total = 55.3 gram