perplexus.info :: Liars and Knights : Doubleton

Doubleton (Posted on 2007-09-20)

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.

See The Solution Submitted by Brian Smith

Rating: 3.5000 (2 votes)

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Solution

| Comment 8 of 9 |

A doubleton's 1st and 3rd statements have opposite truth values.

Carl's first statement (C1) is a lie. Assume he is the doubleton - then C3 is true, which is contradicted by B1. Therefore Carl is not the doubleton.

If Bert is the doubleton, then B1 is false and B3 is true. But B3 would then be contradicted by A2. Therefore Bert is not the doubleton.

Alex is the doubleton.

Posted by tomarken on 2021-02-25 13:00:34

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