It’s another coin riddle!
You are given a standard balance scale and 12 coins that look identical, but one of them is counterfeit and weighs either more or less than the others (you don’t know which). You have writing materials but nothing else.
What is the minimum number of times you need to weigh the coins to identify the counterfeit coin?
Remember, to do this, you’ll just need to determine whether it is heavier or lighter than the others.
To identify the counterfeit coin and determine whether it is heavier or lighter, you need to use a process of elimination.
Here is the simplest solution:
- First, divide the 12 coins into three groups of four coins each. Weigh two of the groups against each other on the scale.
- If the two groups balance, you know the counterfeit coin is in the third group.
- If one of the groups is heavier, you know the counterfeit coin is in the heavier group.
- If one of the groups is lighter, the counterfeit coin is in the lighter group.
- Then, take the group of four coins that contains the counterfeit coin and weigh two coins against two coins on the balance scale.
- If they balance, the counterfeit coin is one of the two remaining coins and is heavier or lighter (depending on whether the first weighing showed it to be heavier or lighter).
- If one of the groups is heavier, that group contains the counterfeit coin.
- If one of the coins is lighter, that group contains the counterfeit coin.
- This leaves you with two coins. Take the remaining two coins and weigh them against each other on the balance scale to confirm which one is the counterfeit coin, by determining whether it’s light or heavier than the other.