# 8.3. Condition:

On an island, there are two tribes: knights, who always tell the truth, and liars, who always lie. Four islanders lined up, each 1 meter apart from each other.

- The leftmost in the row said: "My fellow tribesman in this row stands 1 meter away from me."
- The second from the left said: "My fellow tribesman in this row stands 2 meters away from me."

It is known that there are two knights and two liars in the row. What distances could the third and fourth islanders from the left have named? List all possible options.

## Options for matching:

Third islander $\quad 1$ m

Fourth islander $\quad 2$ m

$3 \mathrm{M}$

$4 \mathrm{M}$

#
# Answer:

The third islander -1 m; 3 m; 4 m.

The fourth islander -2 m.

## Solution.

Let's number the islanders from right to left. Suppose the first one is a knight. Then, from his statement, it follows that the second one is also a knight. However, the second one said that his fellow tribesman is two meters away from him, which is a lie, since the first one, who should be the fellow tribesman of the second, is standing next to him. Therefore, we conclude:

the first one is a liar.

Now, from the first one's statement, it follows that the second one must be a knight, otherwise he would be a liar and the first one would have told the truth. If the second one is a knight, then from his statement, it follows that the fourth one is also a knight. This leaves the third one to be only a liar.