We removed the middle square of $2 \times 2$ from the $8 \times 8$ board. a) How many checkers can be placed on the remaining $60$ boxes so that there are no two not jeopardize? b) How many at least checkers can be placed on the board so that they are at risk all $60$ squares? (A lady is threatening the box she stands on, as well as any box she can get to in one move without going over any of the four removed boxes.)