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?
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Submitted by Gamer
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Rating: 4.0000 (14 votes)
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Solution:
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The way I would solve this is to figure out who is the knight.
If A was the knight, B would be the liar. This means the order for the race is CABD. However, this means C must be a liar as well as B. This can't happen, so A is not the knight.
B is not the knight, or C would be also. (This can be seen from B's first statement.)
If C was the knight, then D would be the knave. Since B came in last place, D's statement about B coming in third place must be a lie. This means C came in second (since D is a knave), and A came in third.
Then, if C is the knight, B must be the liar, which leaves A to be the rebel. This contradicts their statements, so C can't be the knight.
This means D is the knight, which means B is the rebel and this follows the truthfulness of his responses.
All of A's statements are false, so he is the liar, and that leaves C to be the knave. Since his first statement and third statement are false, his second statement must be false. This means A won the race and D lost.
So the final answer is:
1: A, liar
2: C, knave
3: B, rebel
4: D, knight |
