I have 10 bags, each filled with 10 gold coins:
Nine bags have genuine gold coins, each weighing
10 grams. However, one bag has fake gold coins,
with each weighing only 8 grams.
You have a sensitive weighing machine, but you
can use it only once. How will you determine the
bag with the fake gold coins?
Answers
Given:
10 bags with 10 gold coins each.
9 bags have genuine coins weighing 10g each.
1 bag has fake coins weighing 8g each.
To FInd:
The bag with the fake coins by only weighing once
Solution:
Step 1: Label each bag with the number 1 to 10:
Bag 1 will be labeled 1.
Bag 2 will be labeled 2
Bag 3 will be labeled 3 ...
and so on for all the 10 bags
Step 2: Take the number of coins from each bag according to the label:
From bag 1, take 1 coin.
From Bag 2, take 2 coins.
From Bag 3, takes 3 coins ...
and so on for all the 10 bags.
Step 3: Identify the weight if all the coins are real:
Total number of coins = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10
Total number of coins = 55 coins
Total weight if all coins are genuine = 55 x 10
Total weight if all coins are genuine = 550g
Step 4: Weighs all the coins that were taken out:
The weight of a genuine coin = 10g
The weight of a fake coins = 8g
The difference in weight = 10 - 8
The difference in weight = 12g
Assumed the total weight of all the coins take out is n.
The difference in the weight = (550 - n)
Number of fake coins = Difference in the weight ÷ Difference in a coin weight
Number of fake coins = (550 - n) ÷ 2
Step 5: Identify the bag:
The number of fake coins found is the bag that is labeled with that number.