$1\times 2$ dominoes are placed on an $8 \times 8$ chessboard without overlapping. They may partially stick out from the chessboard but the center of each domino must be strictly inside the chessboard (not on its border). Place on the chessboard in such a way: a) at least $40$ dominoes, (3 points) b) at least $41$ dominoes, (3 points) c) more than $41$ dominoes. (6 points) (Mikhail Evdokimov)