Task 4. Six people are standing in a row, each of whom is either a knight (always tells the truth) or a liar (always lies). The first says: "To the right of me, there are exactly five liars," the second: "To the left of me, there is exactly one liar," the third: "To the right of me, there are exactly three liars," the fourth: "To the left of me, there are exactly three liars," the fifth: "To the right of me, there is exactly one liar," the sixth: "To the left of me, there is exactly one liar." Who is who? The numbers of the people are counted from left to right. (20 points)
Answer. From left to right: L, R, L, L, R, L.

Solution. We will call the people the natives of the island of knights and liars.

The first native cannot be telling the truth, because then all people standing to his right would be liars, but in this case, the fifth native would be telling the truth. Therefore, the first native is lying.

Then the second native is telling the truth. From this, it follows that the fourth native is definitely lying, and then the sixth is also lying (there are already at least two liars to his left).

Therefore, the fifth native is telling the truth, and consequently, the third is lying.

Note. Similar reasoning can be applied from right to left.

Criteria. Proven that the first native is lying, and the second is telling the truth - 4 points. Proven that the fourth native is lying - 4 points.

Proven that the sixth native is lying - 4 points.

Proven that the fifth native is telling the truth - 4 points.

Proven that the third native is lying - 4 points.

Similar criteria apply when reasoning from right to left.