Brain Teasers | Counterfeit Coins
Question:
I have10 bags with 100 identical coins in each bag. In all bags but one, each coin weighs 1 gram. However, all the coins in the counterfeit bag weigh either 0.9 or 1.1 grams. Can you help me find the counterfeit bag in only one weighing, using a digital scale that tells the exact weight?
Solution:
We will withdraw 1 coin from the 1st bag, 2 coins from the 2nd bag, 3 coins from the 3rd bag and so on...
Now we have Σ 1 + 2 + …+10 = 55 coins
If there are no counterfeit coins the sum total of weight should be 55 grams.
Let's assume that the xth bag has counterfeit coins
Now the weight would come out to be 55 ± x
For example :
If bag 3 contains counterfeit coins and each of them weigh 1.1 grams
Then the sum total of weight = 1 + 2 + 3*1.1 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55.3
So 55.3 = 55 + 0.3
Hence 3rd bag is counterfeit bag
Similarly, If bag 4 contains counterfeit coins and each of them weigh 0.9 grams
Then the sum total of weight = 1 + 2 + 3 + 4*0.9 + 5 + 6 + 7 + 8 + 9 + 10 = 54.6
So 54.6 = 55 - 0.4
Hence 4th bag is counterfeit bag
Try solving with other numbers and different weights
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Happy Solving :)
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