|
Take the right fork.
First, let's make some generalizations. Suppose you have:
X: Y would say Z is a liar.
If X is a knight, then one of Y or Z is a knight and the other is a liar.
If X is a liar, then Y and Z are both knights or both liars.
In other words, you either have two knights and one liar, or all three liars.
Similarly, for statements such as:
X: Y would say Z is a knight.
If X is a knight, Y and Z are both knights or both liars.
If X is a liar, Y and Z are a liar and a knight, irrespectively.
In general, you must have either one knight and two liars, or all three knights.
Note that in both cases, the order of the people and even which one made the statement is irrelevant.
So, from the statements made, one or three of C, E, and F is a liar.
Since E and F make contradictory statement, they cannot both be knights. Thus, one of them is a liar, and it is still possible that both of them (and C) are liars.
By the same reasoning, one or three of A, B, and C is a liar.
Also, zero or two of B, C, and D is a liar, and zero or two of A, C, and D is a liar.
If we assume that none of B, C, and D are liars, then it's impossible for exactly two of A, C, and D to be liars, so none of them can be. However, that would mean that A, B, and C are knights, but we know that at least one of them is a liar. So, out of the groups of B, C, D and A, C, D, exactly two in each group are liars.
If C is not a liar, then A and D in one group and B and D in the other group must be the two liars. However, that would mean that out of A, B, and C, A and B are liars while C is not, but we know that cannot be the case. So, the assumption that C is a knight is false, and C must be a liar.
At this point, we know the answer. Recall that at least one of E and F is a liar, and either one or three out of C, E, and F are liars. Since C is definitely a liar, all three (C, E, F) must be liars, and the right fork is the one you should take.
For completeness, let's figure out what everyone else is. We know C is a liar, so either D is a liar and A and B are knights, or A and B are liars while D is a knight. Neither case contradicts the fast that either one or three of A, B, C are liars, so we have two equally possible solutions for the people:
A: K L
B: K L
C: L L
D: L K
E: L L
F: L L
In either case, C, E, and F are liars, while A and B are the same, and D is the opposite of whatever they are. No matter what, E and F are not to be trusted (well, you can trust them to lie to you), and you should take the right-hand fork. |
