3. 9 knights and liars stood in a row. Each said that there is exactly one liar next to him. How many liars are there among them, if knights always tell the truth, and liars always lie?
Answer: 3 liars.

Sketch of the solution. Consider the partition of all into groups of people of the same type standing in a row, with people of different types in adjacent groups. In such a group, there can only be one liar. If there are at least two, the extreme liars tell the truth. There are no more than two knights in a group. If there are at least three, the middle knights lie. A group of two knights cannot stand at the edge, otherwise the edge knight lies. A group of one knight can only stand at the edge, otherwise, there are two liars around the knight, and he lies.

Based on these statements, we get that there are two possible arrangements: LRRRLRRRL and RLRRLRRRL. The first one is impossible, as there is a group of two knights at the edge.

Criteria: Answer without justification: 1 point.