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

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.