9.5. In the parliament of the island state of Promenade-and-Tornado, 2019 indigenous inhabitants were elected, who are divided into knights and liars: knights always tell the truth, liars always lie. At the first meeting, 2016 of them sat in the parliamentary seats arranged in the hall in a rectangle of $42 \times 48$, three - in the seats of the chairman and his deputies in the presidium. During the meeting, each one stated that among their neighbors in the seat there are both knights and liars (neighbors are those who sit to the left, right, in front, behind, and diagonally: there can be from 3 to 8 in the hall and 1 or 2 in the presidium). Determine the minimum number of liars at the meeting.
Solution. If two liars are adjacent in the hall, then the entire hall is filled with only liars, which corresponds to the maximum number of liars in the hall. For the minimum number of liars, each liar is adjacent only to knights. The rectangle $42 \times 48$ can be tiled with 224 squares of $3 \times 3$. The minimum number of liars in each such square is 1 (otherwise, if the square contains only knights, the central knight would have lied). Therefore, the minimum number of liars in the hall is 224 (in the centers of the $3 \times 3$ squares). In the presidium - all are liars (three).

Answer: 227.