# 8.2. 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 2 meters away from me."
- The rightmost in the row 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 second and third islanders from the left have mentioned? List all possible options.

## Options for matching:

Second islander 1 m

Third islander $\quad 2 \mathrm{~m}$

3 m

$4 \mathrm{M}$

#
# Answer:

The second islander is 1 m

The third islander is 1 m.

## Solution.

Let's number the islanders from left to right. Suppose the first one is a knight. Then from his statement, it follows that the third one is also a knight; by the principle of exclusion, the second and fourth must be liars. The fourth said that his fellow islander stands two meters away. This is true, but the fourth is a liar, which leads to a contradiction. Therefore, the first one must be a liar.

Notice that a similar situation is created for the fourth and the first: if we look at the row from right to left, the fourth will be the first in it, and the same reasoning will apply to him. That is, the fourth must also be a liar. It follows that the second and third are knights, as the liars are the first and fourth.

From the above, it follows that the second and third are knights, who will say "one meter."