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Three people (Posted on 2011-02-14) Difficulty: 1 of 5
You meet three people, A, B, and C. Each one is either a knight or a liar. A and B make these statements.

A:We are all of the same type.
B:A and C are of different types.

What are A, B, and C?

  Submitted by Math Man    
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Solution: (Hide)
Suppose A is a knight. Then, they are all of the same type, so they are all knights. Then, B would be lying about A and C being of different types. That is impossible, so A is a liar. Therefore, they are not all of the same type, so either B or C is a knight. If B is a liar, then A and C are of the same type, so C is a liar and they are all liars. However, either B or C is a knight. Therefore, B is a knight. Since B is a knight, A and C are of different types, so C is a knight.

A:liar
B:knight
C:knight

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionMike Jones2011-02-15 04:35:07
SolutionspoilerAdy TZIDON2011-02-14 13:32:25
SolutionSolutionhoodat2011-02-14 13:12:12
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