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Let's start by isolating the first two statements made by each native. Note the cyclical nature of the statements:
A: B is a Liar
B: C is a Liar
C: D is a Liar
D: E is a Liar
E: A is a Liar
A: E is a Liar
B: A is a Liar
C: B is a Liar
D: C is a Liar
E: D is a Liar
Assume A is a Knight. Then B and E are Liars. By B's first statement, C is not a Liar, and by E's second statement, D is not a Liar. But C's first statement is a lie, thus C is a Lie-first Knave. Similarly, D's second statement is a lie, so D is a Truth-first Knave.
So by assuming A was a Knight, we determined that A through E in order are Knight - Liar - Lie-first Knave - Truth-first Knave - Liar. It may not be the case that A is the Knight, of course, but due to the cyclical nature of the statements, whoever is a Knight, the next person (cycling around from E to A when necessary) is a Liar, the next is a Lie-first Knave, etc. A little logic and/or trial-and-error should convince you that no matter where you start, this cycle of Knight - Liar - Lie-first Knave - Truth-first Knave - Liar will necessarily always arise, given the above statements. (You may object to the assumption that there is a Knight present at all - take the time to convince yourself that this is the case.)
So now let's look at the next two statements made by each person, once again noting their cyclical nature, and let's continue to assume A is the Knight (and thus B is a Liar, C is a Lie-first Knave, etc.)
A: I'm older than C. TRUE
B: I'm older than D. FALSE
C: I'm older than E. FALSE
D: I'm older than A. TRUE
E: I'm older than B. FALSE
A: I'm younger than B. TRUE
B: I'm younger than C. FALSE
C: I'm younger than D. TRUE
D: I'm younger than E. FALSE
E: I'm younger than A. FALSE
Now that we have assumptions for which statements are true and which are false, we can work out pretty simply the relative order of their ages. From A's two statements, we know that B is older than A, who is older than C. From B's first statment, we know that D is older than B. From E's two statements, we know that E is older than A and younger than B. Thus from oldest to youngest, they are D B E A C.
Sill assuming A is the Knight, let's look at the next two statements made by each person:
A: I finished ahead of D. TRUE
B: I finished ahead of E. FALSE
C: I finished ahead of A. FALSE
D: I finished ahead of B. TRUE
E: I finished ahead of C. FALSE
A: I finished ahead of E. TRUE
B: I finished ahead of A. FALSE
C: I finished ahead of B. TRUE
D: I finished ahead of C. FALSE
E: I finished ahead of D. FALSE
Again, we can work out pretty simply the order in which they finished the race. From A's two statements, we know he was ahead of D and E. From B's first statement we know he finished behind E. From C's first statement we know he finished behind A. Thus A came in first. From D's first statement and C's second statement, we know they both finished ahead of B. Thus B came in last. From D's second statement, we know he finished behind C, and from E's second statement we know he finished behind D. Thus the final order in the race was A C D E B.
In this scenario, then, we find that the oldest person (D) came in 3rd in the race, the 2nd oldest person (B) came in 5th in the race, the 3rd oldest person (E) came in 4th in the race, the 4th oldest person (A) came in 1st in the race, and the 5th oldest person (C) came in 2nd in the race. Of course, this was assuming all along that A was the Knight, which we don't know to be the case.
BUT, once again a little logic and/or trial-and-error should convince you that whoever was the Knight, these same relationships would arise. The names of the people would change, but whoever turned out to be the Knight would end up being the 4th oldest and 1st in the race; the next person after the Knight would be the 2nd oldest and 5th in the race, etc.
So all that remains is to determine who is the Knight. So let's look at the 7th statement made by each person:
A: The oldest person came in 4th place.
B: The 5th oldest person came in 3rd place.
C: The 4th oldest person came in 1st place.
D: The 3rd oldest person came in 2nd place.
E: The 2nd oldest person came in 5th place.
We can now see that A, B and D are lying, and C and E are telling the truth. This is only possible if C is the Truth-first Knave and E is the Knight (which makes A and D Liars and B a Lie-first Knave). We can now re-align our findings from above so that E is the Knight, and we find that from oldest to youngest they are:
Chad, Adam, Dave, Earl, Bart
and from first to last in the race they are:
Earl, Bart, Chad, Dave, Adam. |
