Find The Forged Coin

Weigh the coins, and find out which one is forged

Solution

This is the solution to the Find The Forged Coin game. There are 12 coins. Let's number them, from 1 to 12. Put coins 1-4 to the left, and coins 5-8 right. The result can be one of the following:

Balance tends to the left:
This means that either one of 1-4 is too heavy, or one of 5-8 is too light. So, put coins 1, 2, 5 and 6 to the left and coins 3, 7, 9 and 10 to the right.
- Balance tends to the left:
  So, either coin 1/2 is too heavy, or coin 7 is too light. Let's weigh coin 1 left and 2 right:
  - Balance tends to the left:
    Coin 1 is too heavy
  - Balance tends to the right:
    Coin 2 is too heavy
  - The load is equal on both sides:
    Coin 7 is too light.
- Balance tends to the right:
  This is left as an excercise to the reader. This case is very similar to the previous case.
- The load is equal on both sides:
  So, either coin 8 is too light, or coin 4 is too heavy. Let's weigh coin 1 left and 8 right:
  - Balance tends to the left:
    Coin 8 is too light.
  - Balance tends to the right:
    Impossible! This will not happen...
  - The load is equal on both sides:
    Coin 4 is too heavy.
Balance tends to the right:
This is left as an excercise to the reader. This case is very similar to the previous case.
The load is equal on both sides:
You have only 4 suspicious coins left, and two times left to weigh. You should be able to do this yourself, don't you think?

dotSphinx

Find The Forged Coin

Solution