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| Doubleton (Posted on 2007-09-20) |
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Alex, Bert and Carl are all different types. One is a knave, one is either a knight or liar, and one is a doubleton. A doubleton is a type similar to a knave, except that a doubleton's truth pattern is two true statements followed by two false statements repeatedly.
From the statements below, determine who is the doubleton.
Alex:
1. I am a knight.
2. Bert is the doubleton.
3. Carl is the knave.
Bert:
1. I am the knave.
2. Carl is the doubleton.
3. Alex is a liar.
Carl:
1. I am a liar.
2. Alex is the doubleton.
3. Bert is a knight.
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Submitted by Brian Smith
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Rating: 3.5000 (2 votes)
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Solution:
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Note that the first and third statements made by a doubleton are opposite, one is true and the other is false.
If Alex's first statement is true then Bert's first and third statements would have to be false, which implies Bert is not the doubleton, contrary to Alex's second statement. Therefore Alex's first statement is false and Alex is not a knight.
A knight would not make either of Bert's or Carl's first statements, therefore no one is a knight. The three are a knave, a liar, and a doubleton, in some order.
Carl's first statement is false since a liar would never admit to being a liar, which means Carl is not the liar. Since Carl's third statement is also false he must be the knave, making Alex the doubleton and Bert the liar.
Statement Summary:
Alex: F, F, T
Bert: F, F, F
Carl: F, T, F |
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