A, B and C are worth 1, 2 and 3 although we don't know which letter each value corresponds to. To find out, they give us the following clues:

- If A is not 1 then C is not 3
- If B is 1 or 2 then A is 3
- If C is not 2 then A cannot be 3
- If C is not 1 then A is not 3
- If C is 3 then B is not 1 or 2
- If B is 3 then A is not 2

#### Solution

**A = 1, B = 3 and C = 2**. To reach this conclusion we can apply the following reasoning:

The second track gives us two possibilities: B = 2, A = 3 and C = 1 or B = 1, A = 3 and C = 2 but the tracks (3) and (4) make these results impossible.

Rule (4) gives us two possibilities: B = 2, A = 1 and C = 3 or B = 1, A = 2 and C = 3 but track (5) makes these results impossible.

Then, from track (5) we see that if B = 3 then A which cannot be 2, it has to be 1 and therefore C = 2.