8.5. In the parliament of the island state of Promenade-and-Tornado, only the indigenous inhabitants of the island can be elected, who are divided into knights and liars: knights always tell the truth, liars always lie. A secret ballot on 8.09.19 re-elected 2019 deputies. At the first meeting, all deputies were present: 2016 of them sat in the deputies' chairs, arranged in the hall in a rectangle $42 \times 48$, three - in the chairs of the chairman and his deputies in the presidium. During the meeting, each one stated that among his neighbors in the chair were only liars (neighbors - 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 knights in the parliament.
Solution. A rectangle $42 \times 48$ can be tiled with $3 \times 3$ squares (224 are required). In each such square, there must be at least one knight (otherwise - if the square contains only liars, the liar in the central cell would have told the truth, which is impossible). Thus, the minimum number of knights in the hall is 224 (in the centers of the squares with which we tiled the rectangle - in this case, all knights in the hall told the truth, and all liars lied as they should). The minimum number of knights in the presidium is 1 (in the center).

Answer: 225.