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 A Logic Accusation (Posted on 2003-10-01)
In an island peopled by Knights (who always say the truth) and Liars (who obviously always lie), two persons spoke about each other.

A said: "B would say I lie."

B said: "That is true."

Can anything be deduced as to what kind is each of them?

 See The Solution Submitted by Federico Kereki Rating: 2.8667 (15 votes)

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 Puzzle Solution With Explanation | Comment 16 of 17 |

Assume that A is a Knight, then it follows that B would indeed accuse A of being a liar. Accordingly, B's statement would be false in that situatuation, so that B would be a liar.

Assume that A is a liar. Then, it follows from A's false statement
that B would in reality, say that A is not a liar. But, this is false
since at the outset, we have assumed that A is a liar. Consequently, B is a liar.

Comparing the two cases , it follows that B is a liar. Now, a Liar
will always identify a fellow Liar as Knight and will identify a
Knight as a Liar. Since, B has identified A's statement as a truthful one ,  it now follows that B must be a liar.

 Posted by K Sengupta on 2008-03-28 05:41:01

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