# 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?