You meet four people, A, B, C, and D. One of them is a knight, one is a liar, one is a knave, and one is a normal who tells the truth and lies at random. They make the following statements.
A:I am a liar.
A:C is a normal.
B:D is a knight.
C:B is a knave.
What are A, B, C, and D?
First conclusions:
A is either normal or a knave.
If A is a knave then C is normal.
B is not a knight.
Secondary conclusions:
Try A is a knave and C is normal. Since B is not a knight then D must be the knight, leaving B as the liar. But B said D is a knight; a liar wouldn't make that true statement, so this is not the scenario.
So A is normal. B is not a knight, so either C or D is the knight. If C is the knight, then B is the knave and D is the liar. This seems sound, but is it the only scenario that works?
If D were the knight, B and C would be knave and liar, not necessarily in that order. But either order would lead to a contradiction.
Therefore:
A is normal, and telling two lies.
B is a knave telling a lie.
C is the knight.
D thus is the liar.
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Posted by Charlie
on 2022-09-03 08:28:47 |
solution