2

9.

Again three people A, B, and C. A says, “B and C are of the same type.”You then ask C,
“Are A and B of the same type?”What does C answer?

10. You come across two inhabitants of the island, A and B, resting under a tree. You ask A, “Is
either of you a knight?”He answers, and you know the answer to your question. What are A
and B?

11. While traveling on the island of knights and knaves, you decide to visit a courtroom there
and observe a court case being tried. On the way there your guide informs you that there has
recently been a large immigration from the island of normals (you know your guide is a
kinght, so you can trust him). On the island of normals, a person might sometimes tell the
truth, and sometimes lie. When you arrive at the court, you find the defendant, the
prosecutor, and the defense attorney. In previous sessions, it has been established that among
the three people, one is a knight, one is a normal, and one is a knave. Furthermore, one of
the three is definitely guilty of the crime, and the other two innocent, but it is known that the
guilty one is not the knave. The three make the following statements in court:

Defendant: I am innocent.
Defense Attorney: My client is indeed innocent.
Prosecutor: Not true, the defendant is guilty.
The jury convene, but cannot come to any decision. So you decide to take a crack at the
case. You ask the prosecutor, “Are you the guilty one?” and he answers. Then you ask the
defendant, “Is the prosecutor guilty?” and he answers. From this you deduce everything.
Who is guilty, who is normal, who is the knight, and who is the knave?

12. On the last stop of your tour, you come to the sacred temple of knights and knaves. In the
center chamber are four doors, X, Y, Z, and W. Your guide tells you that at least one of the
doors leads to a treasure room, and the others to a fierce dragon. If you can deduce which
door leads to the treasure, you will be presented with an item from the collection as a present.
Standing at the doors are eight priests, A, B, C, D, E, F, G, and H, who are either knights or
knaves (no normals have yet risen to the rank of high priest at the temple). They make the
following statements:
A: X is a good door.
B: At least one of the doors Y and Z is good.
C: A and B are both knights.
D: X and Y are both good doors.
E: X and Z are both good doors.
F: Either D or E is a knight.
G: If C is a knight, so is F.
H: If G and myself are both knights, so is A.
Which door do you choose?