# Finding the Bag of Fake Coins

## How to identify the bag of fake coins with only one weighing?

Imagine having ten bags of 100 coins each, one containing fake coins that weigh 4.5 grams instead of 5 grams like the real coins. Using a modern scale that provides precise weight measurements, how can you find the bag of fake coins in just one weighing?

One possible solution to this problem is to number each bag from 1 to 10. Then, place 1 coin from bag 1, 2 coins from bag 2, 3 coins from bag 3, and so on, until you place 10 coins from bag 10 onto the scale. If all the coins were real, the total weight would be a multiple of 5 grams. However, since one bag contains fake coins that weigh 4.5 grams, the total weight will not be a multiple of 5 grams. By analyzing the weight discrepancy, you can identify the bag containing the fake coins.

To solve this problem, let's break down the steps involved in finding the bag of fake coins in just one weighing:

## Step 1: Number the Bags

Start by numbering each bag from 1 to 10 for easy reference.

## Step 2: Place Coins on the Scale

Begin by placing 1 coin from bag 1, 2 coins from bag 2, 3 coins from bag 3, and so on until you place 10 coins from bag 10 onto the scale.

## Step 3: Analyze the Weight

If all the coins were real, the total weight would be a multiple of 5 grams (e.g., 5g, 10g, 15g, etc.). However, since one bag contains fake coins weighing 4.5 grams, the total weight will deviate from the expected multiples of 5 grams. The discrepancy in weight will indicate which bag contains the fake coins.

By following this method, you can successfully identify the bag of fake coins with just one weighing, thanks to the precise measurements provided by the modern scale.