2008_Question6

I’ll be honest, I prefer when people are just called by letters in questions.

i) A cannot be a saint, as he would have then lied.
A cannot be a liar, as he would have said the truth.
Thus, A is a switcher.
B is thus lying, and is the liar (C is thus the saint).

ii) If P is lying, then Q is either a saint or a contrarian. In either case, Q, in this instance, would tell the truth, thus R is the liar. Ergo, P is the contrarian and Q is the saint.

If P is telling the truth, then Q is the liar. However, R would also lie, but neither P nor R can be the contrarian. Hence, P cannot tell the truth in this instance.

Therefore, we deduce R is the liar.

iii) Interesting case we have here;

If X starts by telling the truth, then Y is a liar. Z cannot be a contrarian because he is lying. But X cannot be either because he is telling the truth. We have a contradiction!

Thus, X begins by lying. Hence, Y is not a liar.

If Y begins by telling the truth, then Z is a liar. Y is not a contrarian so X must be. Y is thus a switcher. This would imply X lied in his second statement, which is contradictory to the fact that he must be a contrarian.

Ergo, Y also begins by lying. Hence, Z is not a liar. This leaves X to be the liar.

Footnote:

We note that Y cannot be the contrarian, as Y lied after a lie. Hence, Z is the contrarian and Y is a switcher.

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