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Old 04-23-2010, 12:34 AM   #11
I hit open jumpers.
Join Date: Jun 2006
Posts: 1,167
Default Re: Brain Teasers and Riddles

In an island there are 2 type of people, knaves and knights. Knaves always lie, and knights always tell the truth.
You encounter 2 people. Person A and Person B.

A: "I'm a knave or B is a knight".
B doesn't say anything.

Determine what A is and what B is (Knight or Knave). If not possible to determine, say so.

There are only four cases.

Case 1: Suppose both A and B are knaves. Then one part of A's statement is true, even though B is not a knight. Since his statement has an "or", only one part needs to be true for A to be telling the truth. Hence A is telling the truth. But this contradicts the fact that he's a knave and is supposed to lie. Hence case 1 is impossible.

Case 2: Suppose A is a knave and B is a knight. Then again, A's statement would be a true statement, which contradicts his job, as a knave, to lie. Hence case 2 is impossible.

Case 3: A is a knight, B is a knave. Now both parts of A's statement is false; i.e. A is not a knave and B is not knight. Hence A is lying, and this contradicts the fact that he is a knight. Hence case 3 is impossible.

Case 4: A is a knight, B is a knight. Now A's statement is correct, since B is a knight. This makes sense because A should be telling the truth. Hence both A and B are knights, and this case is the only possibility.
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