A logic problem by Rakibul Hasan Emon

Logic Level 3

There are 10 bags of coins. Each bag contains 10 coins identical in appearance, but one of the bags' coins are all counterfeit. So there is no way to visually identify the bag of counterfeit coins, but you are given the clue that the counterfeit coins are each 1 gram more in mass than the real coins. With a scale at your disposal that directly measures the mass of whatever is placed on it, what is the fewest number of weighings required to determine which bag has the counterfeit coins?

Note: You are allowed to take any number of coins out of any of the bags.

1 2 3 4

Rakibul Hasan Emon by Rakibul Hasan Emon , 20, Bangladesh

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2 solutions

Roger Erisman
Jan 23, 2017

Number the bags 1 to 10.

Take as many coins out of each bag as its number: 1 out of #1, 2 out of #2, etc.

Weigh all the coins that were removed at the same time.

The difference between what they weigh and what they should weigh will be the bag number of the counterfeit coins.

The weight they should weigh if all were real is 55 * weight of 1 real coin, whatever that is.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

From where do we get 55 real coins to weigh/compare against?

Anirudh Saha - 4 years, 4 months ago

The answer should be 2 and not 1.

Ankit Kumar Jain - 4 years, 3 months ago
Ankit Kumar Jain
Mar 15, 2017

If we know the true weight , then we can do it in 1 time only.

Suppose from bag 1 , I take out 1 coin , from bag 2 , 2 coins and so on.

Then weighing them together and comparing with what it should be will give us the desired result.

But since , we don't know the original mass , hence we need 2 steps.

First , we will take any coin from any bag and weigh it. Now , as in the previous case , we take up coins and calculate the average of the 55 coins.

Now , comparing the two values , if the average is greater than the individual :

We multiply the individual mass by 55 55 and subtract it from the mass of the 55 55 balls together which tells us the required answer.

In the other case when the individual mass is greater than the average mass clearly indicates that it is the bag with counterfeit coins.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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