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?
A 1st liar
B 3rd rebel
C 2nd knave
D 4th knight
Start with who is the knight.
B is not the knight due to statement B1. True or False, B is not the knight.
C is not the knight. If C is the knight, D is the knave. Statement D3 must be False since it does not agree with C3. So D1 must also be False. This means that B must be the liar, and statement B1 is False. So C is not the knight.
A is not the knight. If A is the knight, B is the liar, and either C or D is the knave. If C is the knave, then C1 is False, making C2 True. However, C2 is False since it disagrees with A2. Then C is not the knave. If D is the knave, then D1 conflicts with A1 and must be False. Then D2 must be True, but it disagrees with A2. Then D is not the knave and thus A is not the knight.
D is the knight.
This leads to:
B is the rebel, C is 2nd, B is 3rd.
A's statements become F,F,F - A is the liar
B's statements are F,F,T - B is the rebel
C's statements are F,X,F - C is the knave and C2 is True
Filling in the matrix
A 1st liar
B 3rd rebel
C 2nd knave
D 4th knight
Solution
