Knights always tell the truth. Liars always lie. Knaves alternate between telling the truth and lying. Pages tell the truth if the last statement was a lie and lie if the last statement was a truth. Squires tell the truth if the last statement was a truth and lie if the last statement was a lie. You meet five people, A, B, C, D, and E. One of them is a knight, one of them is a liar, one is a knave, one is a page, and one is a squire. They make the following statements.
A:I am a liar.
B:I am a liar.
C:I am a squire.
D:A is a page.
A:E is not a knight.
What are A, B, C, D, and E?
E is a knight.
Nobody can truthfully say "I am a liar", so the first two statements are lies and neither A nor B is a knight. C can't be a knight either because claiming to be a squire would be a lie.
If D's statement is false, then D is also not a knight, but there's a knight in the group, so it must be E.
If D's statement is TRUE, then A is a page, and since pages follow truth with lies, A's second statement is a lie and E really is a knight.
The first three statements are all lies, since a squire can't follow a lie with the truth and nobody can truthfully claim to be a liar. Since a page follows a lie with the truth, the page can't be B or C. If D were the page then A would also have to be a page and there's only one page in the group. So D is not a page, and A is the page.
Since A is indeed a page, D's statement is true. Among the remaining types, only a Knave could make a true statement following a false one, so D is a Knave.
That leaves B and C. B can't be a liar (having claimed to be one), so C is the liar and B is by elimination the squire.
Final:
A - page
B - squire
C - liar
D - knave
E - knight
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Posted by Paul
on 2020-10-10 11:10:48 |
slightly different solution (unique)
