Friday, April 12, 2013

Amy: The Innocent Knight

Last night my friend showed me this tricky question.

Suppose that on an island there are three types of people, knights, knaves, and normals (also known as spies). Knights always tell the truth, knaves always lie, and normals sometimes lie and sometimes tell the truth. Detectives questioned three inhabitants of the island—Amy, Brenda, and Claire—as part of the investigation of a crime. The detectives knew that one of the three committed the crime, but not which one. They also knew that the criminal was a knight, and that the other two were not. Additionally, the detectives recorded these statements: Amy: "I am innocent." Brenda: "What Amy says is true." Claire: "Brenda is not a normal." After analyzing their information, the detectives positively identified the guilty party. Who was it?

My solutions:
Assuming the two of three people are either a Knave or Normal.


Amy
Brenda
Claire
         i.             
Knight
Knave
Normal
       ii.             
Knight
Normal
Knave
      iii.             
Knave
Knight
Normal
     iv.             
Knave
Normal
Knight
       v.             
Normal
Knight
Knave
     vi.             
Normal
Knave
Knight

i and ii is wrong because a Knight cannot be innocent. iii and  iv is wrong because a Knight gave false statement. v is wrong because a Knave gave true statement. This leaves the last option where Amy(Normal) tells a lie, Brenda(Knave) approves Amy's lie and Claire(Knight) gave a true statement.

Assuming the two of three people are Normals.


Amy
Brenda
Claire
         i.             
Knight
Normal
Normal
       ii.             
Normal
Knight
Normal
      iii.             
Normal
Normal
Knight

i is wrong because a Knight cannot be innocent. iii is wrong because a Knight gave a false statement. This leaves the second where Amy(Normal) tells a truth, Brenda(Knight) approves Amy's statement and Claire(Normal) gave a true statement.

Assuming the two of three people are Knaves.



Amy
Brenda
Claire
         i.             
Knight
Knave
                 Knave
       ii.             
Knave
Knight
Knave
      iii.             
Knave
Knave
Knight

is wrong because a Knight cannot be innocent. ii is wrong because a Knave gave a true statement. This leaves the last options where Amy(Knave) tells a lie, Brenda(Knave) approves Amy's lie and Claire(Knight) gave a true statement.

haha, kesian Claire.
Comments and critics are welcomed.

1 comment:

  1. Assuming two of three people are a Knave or Normal
    The last option isn't correct. If Amy is Normal and tell a lie then Amy would be cruiminal but only knight can be criminal. The only option correct would be Amy is Normal and tell the truth

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