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

i 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.
Assuming two of three people are a Knave or Normal
ReplyDeleteThe 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