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X and Y (Posted on 2011-01-04) Difficulty: 3 of 5
There is an island where every inhabitant is either of Type X or Type Y. One of the types always tells the truth, and the other type always lies, but you are not sure which is which. You meet two inhabitants of this island, A and B.
A: B is of Type X.
B: We are both of Type Y.
Which type tells the truth, which type lies, and what are A and B?

See The Solution Submitted by Math Man    
Rating: 4.0000 (2 votes)

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Solution Another method Comment 3 of 3 |
Assume Type X is knight and Type Y is liar; this leads to the following contradiction:

If B said "We are both liars", he can't be a Knight, so he must be a liar and A is a knight. But then A would make the untrue statement "B is a knight".

Thus, Type X is a knight and type Y is liar.

So A claims B is a liar, which means they are of opposite types. Thus B must be lying, which means A is a knight and B is a liar

  Posted by Gamer on 2011-01-05 15:21:01
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