In detail

The horse race

The horse race

Horse racing was the favorite sport of the Romans, and it was very competitive. In a very close race there was only a small distance between the first, the second and the third. Among them was one that always lied, one that alternated between lying and telling the truth and the other one always telling the truth. Each one affirmed a different thing:

TO
- I've been the first
- B has been the second
- C has been the second

B
- I've won
- I've been first all the way
- C was behind A and I

C
- I've won
- A was far behind when I crossed the finish line
- B has finished before A

Could you say who lies, who tells the truth and who alternates between them in an unknown order or if on the contrary there is more than one who lies, tells the truth or alternates between them?

Solution

We assume that A is the winner. In that case your first and third statements are true. Then his third statement coincides with the third of B, which means that the first and third statements of B are correct, that would mean there would be two winners. Therefore as that could not be, C would be the winner.

The third statement of C is aware of the second statement of A. That means that A lies in his first statement but instead tells the truth in his second statement. Then B lied all three times since we knew that the race was very close. A and C alternated between lying and telling the truth, but B always lied.