Four athletes, Ann, Bea, Carol, and Dorothy went out one morning and ran a race. At the end of the race, the following statements were made:
Ann: "I didn't come in first or last."
Bea: "I didn't come in last."
Carol: "I was first."
Dorothy: "I was last."
It is known that one, and one only, of the four athletes is the liar while the other three are knights.
Who won the race?
Assume A is the liar. Then C and D are telling the truth, and came in first and last, which means A is not lying. Contradiction.
Assume B is the liar. Then B came in last, but so did knight D. Contradiction.
Assume D is the liar. Then nobody came in last. Contradiction.
So, C is the liar. C did not come in first, but neither did A or D. So B came in first. D came in last, and A & C came in 2nd and 3rd (or 3rd and 2nd).
While we don't know the complete order, we do know that Bea won the race.
Liars don't prosper (spoiler)
