You want to know the out come of a race between 4 people who live in Race Town and ask the outcome of the race. Each of the four people give three statements.

Among these four people there is one knight (who always tells the truth), a liar (who always lies), a knave (who tells the truth and lies alternatingly), and a rebel. The rebel doesn't like the truth patterns of the other three, and will never follow the order of them. (So the rebel will say at least one thing false, and one thing true, but not in an alternating way.)

A: B is the liar.
C won the race.
I came in second.

B: C is the knight.
I came in last place.
C came in second.

C: D is the knave.
A won the race.
B came in last place.

D: B is the rebel.
C came in second place.
B came in third place.

Using this information, what is each person's type and in what order did they finish in the race?

I think I have it. I began by trying to figure out who the knight is. It has to be A, C, or D (B said C was the knight, so it can't be B). If A was the knight, B had to be the liar. D could not have been the knave because A contradicted both his second and third statements, so D was the rebel and C the knave. If C was the knave his first statment was false since he said D was the knave. So, his second statment (A was 1st)would have to be true, but it contradicts A's second statement (that C was 1st).

So the knight was C or D. If it were C, however, D would be the knave. His third statement would have to be false (it contradicts C's third statement), so the first must be false (therefore B couldn't be the rebel, so A is and B is the liar) and the second true. However, B's second statement was that C is the knight, which would have to be true, so this doesn't work.

So, D is the knight, and he says that B is the rebel. B's first statement is false (that C is the knight), and his second statement (that B was 4th) contradicts D's statement that B was third), so it has to be false. So, B's third statement (that C was 2nd) must be true, and we already knew it anyway because D said so. A cannot be the knave because D's second statement contradicts both A's 2nd and 3rd statements. So, A is the liar and C is the knave. We know from D the knight that C was 2nd and B was 3rd. Knave C's first statement (that D was the knave) was false, so the second (A was first) must be true. So A was first, B was third, C was second, and by process of elimination D was 4th.

Posted by Sam on 2004-01-07 12:45:45