Question 46
An $L$ is an arrangement of $3$ adjacent unit squares formed by deleting one unit square from a $2 \times 2$ square. How many $L$s can be placed on an $8 \times 8$ board (with no interior points overlapping)? Show that if any one square is deleted from a $1987 \times 1987$ board, then the remaining squares can be covered with $L$s (with no interior points overlapping).