155. 

From the Middle Sanctuary, one can exit through four doors $\mathrm{X}, \mathrm{Y}, \mathrm{Z}$, and $\mathrm{W}$. At least one of them leads to the Inner Sanctuary. Those who exit through another door are devoured by a fire-breathing dragon.

In the Middle Sanctuary, during the trial, there are eight priests A, B, C, D, E, F, G, and H, each of whom is either a knight or a liar. The priests told our philosopher the following.

A: X is the door leading to the Inner Sanctuary.

B: At least one of the doors Y and Z leads to the Inner Sanctuary.

C: A and B are knights.

D: Both doors X and Y lead to the Inner Sanctuary.

E: Both doors X and Y lead to the Inner Sanctuary.

F: Either D or E is a knight.

G: If C is a knight, then F is a knight.

H: If G and I myself are knights, then A is a knight.

Which door should the philosopher choose?
155. First, let us prove that $G$ is a knight. For this, it is sufficient to prove that his statement is true, that is, if $\mathrm{C}$ is a knight, then $\mathrm{F}$ is also a knight. We will prove this by deriving the conclusion "F is also a knight" from the premise "C is a knight."

So, suppose that C is a knight. Then A and B are both knights. Therefore, $\mathrm{X}$ is the door leading to the Inner Sanctuary, and either door Y or door $Z$ leads to the Inner Sanctuary.

Case 1: Door Y leads to the Inner Sanctuary. Then both doors $\mathrm{X}$ and Y lead to the Inner Sanctuary. In this case, $\mathrm{D}$ is a knight.

Case 2: Door $Z$ leads to the Inner Sanctuary. Then both doors $\mathrm{X}$ and $\mathrm{Z}$ lead to the Inner Sanctuary. In this case, $\mathrm{E}$ is a knight.

Thus, either D or E must be a knight. Therefore, the statement made by F is true, so $\mathrm{F}$ is a knight.

So, from the premise "C is a knight," we have derived the conclusion "F is a knight." Therefore, it is true that if $\mathrm{C}$ is a knight, then $\mathrm{F}$ is a knight. This is exactly what G claimed. Hence, G is a knight.

Now let us prove that the statement made by $\mathrm{H}$ is true. According to H, if $\mathrm{G}$ and $\mathrm{H}$ are both knights, then A is a knight. Suppose that H is a knight. Then G and $\mathrm{H}$ are both knights. Moreover, it is true that if $\mathrm{G}$ and H are both knights, then A is a knight (this is what H claimed, and he is a knight by assumption). Therefore, if $\mathrm{H}$ is a knight, then 1) G and H are knights; 2) if $\mathrm{G}$ and $\mathrm{H}$ are knights, then A is a knight. From (1) and (2), it follows that A is a knight. Thus, if $\mathrm{H}$ is a knight, then A is a knight. This is exactly what $\mathrm{H}$ claimed, so H must be a knight. His statement is true, and since G and H are knights, A is a knight.

Thus, we have established that A is a knight. Therefore, door X indeed leads to the Inner Sanctuary, and our philosopher should choose door $X$.