# Find the Bag With Defective Coins

# 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.

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