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Legally Blonde (Posted on 2016-12-19) Difficulty: 1 of 5
You meet three blonde women, A, B, and C. Each of them is either a knight or a liar. Exactly one of them is Elle Woods.

A:I am Elle Woods.
B:I am Elle Woods.
C:At least two of us are liars.

What are A, B, and C, and who is Elle Woods?

No Solution Yet Submitted by Math Man    
Rating: 3.0000 (2 votes)

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Solution Explanation for Puzzle Answer Comment 10 of 10 |
(In reply to Puzzle Answer by K Sengupta)

 A and B cannot both be named "Elle Woods" and therefore Knights, the possibilities are:

(A,B) = (knight, liar), (liar, knight), (liar, liar) 
Accordingly, at least one amongst A and B must be a liar. ,,,,,,,,,, (i)

Assume that C is a liar. Then  his false statement implies that at most one of A, B, and C is a liar.
But, if C is a liar, then from (i) , we observe  that at least  two of A,B, and C is a liar. Contradiction. 
Accordingly, C is a knight and C's true statement implies that each of A and B is a liar and therefore, none of them is named "Elle Woods". 
Consequently,  C must be Elle Woods, where A and B are both liars and C is a knight.

Edited on February 28, 2022, 12:55 am
  Posted by K Sengupta on 2022-02-28 00:46:37

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