# Find the Bag With Defective Coins

How to find a Bag with defective Coins?

We have 10 bags of 1 Rupee coins. One bag contains all the defective coins,

the weight of each coin in that bag is 1 gram lesser than the weight of a normal 1 Rupee coin.

You have a spring balance,

which tells the exact weight. After how many minimum no

. of weighs you can separate the bag with defective coins.

Answer to the defective coin problem

The minimum no. of weighs required is one.

This is how we arrive at the answer.

Let the weight of a normal 1 Rupee coin is R.

Now number the bags from 1 to 10 and take out the no. of coins equal to bag’s number from each bag, for example from 1st bag, take one coin, from 2nd, take 2 coins and from 5th bag take 5 coins and so on and so forth.
Let D be the number of the bag which contains the defective coins.

Now put all the coins on spring balance and weigh them. Read the spring balance reading, say it is W grams.
Then W = (R grams)*(1+2+3….+10) – D*(1 gram)
D will come out to be a number between 1 to 10 and that’s the required bag number with the defective coins.