6.5. In the castle, there are 16 identical square rooms forming a $4 \times 4$ square. Sixteen people, who are either liars or knights (liars always lie, knights always tell the truth), moved into these rooms, one person per room. Each of these 16 people said: "At least one of the rooms adjacent to mine is occupied by a liar." What is the maximum number of liars that could be among these 16 people? Rooms are considered adjacent if they share a wall.
Answer: 8 liars.

Solution: Note that liars cannot live in adjacent rooms (otherwise, they would be telling the truth). Let's divide the rooms into 8 pairs of adjacent rooms. Then, in each pair, there can be no more than one liar. Therefore, there can be no more than 8 liars in total. Consider a chessboard coloring of the rooms in black and white. If we place 8 liars in the "black" rooms and 8 knights in the "white" rooms, the condition of the problem will be satisfied (all liars will be lying, and all knights will be telling the truth).

Comment: A correct answer without justification - 0 points.

Example of placing 8 liars and 8 knights - 2 points.

Proven that there are no more than 8 liars - 5 points.