There are 10 bags full of coins, with infinite coins in each bag. But one bag is full of forgeries, and you can’t remember which one. But you do know that genuine coins weigh 1 gram and forgeries weigh 1.1 grams. You have to identify that bag in minimum readings. You are provided with a digital weighing machine.


Updated: Nov. 27, 2020 — Training Time: 2 minutes
Overseen by: Archangel Macsika

Topic: Data Science.

Difficulty: Intermediate.

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Objective: There are 10 bags full of coins, with infinite coins in each bag. But one bag is full of forgeries, and you can’t remember which one. But you do know that genuine coins weigh 1 gram and forgeries weigh 1.1 grams. You have to identify that bag in minimum readings. You are provided with a digital weighing machine.

Short Answer: practical answer.

Full Solution

This follows same procedure as the 5 jars of pills puzzle we tackled earlier.

First, we will take 1 coin from the first bag, 2 coins from the second bag, 3 coins from the third bag and so on till we take 10 coins from the 10th bag.

The total number of all coins taken out will be:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55 coins.

Next, we weigh the 55 coins together. If they are all genuine, then we will have 55 grams.
However, the question dictates the presence of a bag full of forgeries.
Bear in mind that each contaminated pill has a difference of 0.1 gram.

If the weight is 55.1, then the forgery coins is in the first bag since we took 1 coin weighing 1.1 gram.

If the weight is 55.2, then the forgery coins is in the second bag since we took 2 coins weighing 1.1 gram.

If the weight is 55.3, then the forgery coins is in the third bag since we took 3 coins weighing 1.1 gram.

... and so on.

If the weight is 56.0, then the forgery coins is in the tenth bag since we took 10 coins weighing 1.1 gram.

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