Well done for taking on this tricky puzzle! Let’s unravel the mystery and figure out how to determine the number of counterfeit coins using the digital scale only once:
The Solution
Step 1: Number the Coins
Label each coin in the bag with a number from 1 to 100.
Step 2: Select Coins to Weigh
Take 1 coin from the first pile, 2 coins from the second pile, 3 coins from the third pile, and so on, until you have 100 coins from the 100th pile. This means the total number of coins you are weighing is:
1 + 2 + 3 + … + 100 = 5050 coins.
Step 3: Calculate the Expected Weight
If all the coins were real, the total weight would be:
5050 coins × 10 grams = 50500 grams.
Step 4: Measure the Actual Weight
Place all the selected coins on the digital scale and record the actual weight. Let’s call this value X.
Step 5: Find the Difference
The difference between the expected weight and the actual weight will reveal the number of counterfeit coins. Calculate the difference:
50500 grams – X = Y grams.
Since each counterfeit coin is 1 gram lighter, the number of counterfeit coins is:
Y (grams) = Number of Counterfeit Coins.
Example
If the scale reads 50475 grams, the difference is:
50500 – 50475 = 25 grams.
This means there are 25 counterfeit coins in the bag.
Why Does This Work?
By taking a specific number of coins from each pile (corresponding to their label), the weight loss directly correlates to the number of counterfeit coins. Each lighter coin subtracts 1 gram, making the difference easy to calculate.
Congratulations! You’ve cracked the coin conundrum. Ready for the next challenge? Keep exploring TQ for more brain-bending puzzles! 😊