Bag of Coins Puzzle
Bag of Coins Puzzle
Imagine you are presented with a set of 10 different bags, and each of these bags contains exactly 1,000 coins. Among these 10 bags, nine of them are filled entirely with genuine coins, while one of the bags contains counterfeit coins. At first glance, all the coins—whether real or fake—appear completely identical in terms of size, shape, and appearance.
However, there’s one subtle difference that distinguishes the counterfeit coins: each genuine coin weighs exactly 1 gram, while each counterfeit coin is slightly heavier, weighing 1.1 grams. You are provided with a precision weighing scale that can measure weight accurately.
What is the minimum number of times you need to weigh the bags to figure out the bag with the forged coins?
Bag of Coins Puzzle
Imagine you are presented with a set of 10 different bags, and each of these bags contains exactly 1,000 coins. Among these 10 bags, nine of them are filled entirely with genuine coins, while one of the bags contains counterfeit coins. At first glance, all the coins—whether real or fake—appear completely identical in terms of size, shape, and appearance.
However, there’s one subtle difference that distinguishes the counterfeit coins: each genuine coin weighs exactly 1 gram, while each counterfeit coin is slightly heavier, weighing 1.1 grams. You are provided with a precision weighing scale that can measure weight accurately.
What is the minimum number of times you need to weigh the bags to figure out the bag with the forged coins?
Solution
- We are allowed to weigh the bags only once to figure out the forged bags.
- Let us number the bags, from bag 1 to bag 10.
- Now from bag 1, we take 1 coin, and from bag 2 we take 2 coins, from bag 3 we take 3 coins, and so on.
- Now we take all these coins and weigh them together.
- Between all the 10 bags we will have 55 coins.
Now we know that the real coins all weigh 1 gram while the forged coins weigh 1.1 gram or have an extra 0.1 gram of weight.
Therefore by observing the extra weight in our picked coins, we can figure out the forged bag.
Say the weight of the collective coins comes as 55.5 grams. Then we can say that there is an additional 0.5-gram weight, which is , therefore bag 5 from where we took 5 coins is the forged bag.
Similarly, if the weight was 55.7, then it would be bag 7. To sum it up, if the weight is 55, then the bag numbered n is the bag with the forgeries.
Also Check:
- Flipping Coins Puzzle Answernswer
- 3 Glass & 10 Coins Puzzle Answer
- Pirates and 100 Coins Puzzle Answer
- Horse Puzzle Answer
- Handshake Puzzle Answer
- Burning Rope Puzzle Answer
- Shopkeeper & the fake note Puzzle Answer
- Heavier Ball Puzzle Answer
- 5L measuring Puzzle Answer
- 6 Digit number Puzzle Answer
- Gold Bar Puzzle Answer
Login/Signup to comment