Question 2
The rows and the columns of a $16 \times 16$ table are labeled from $1, 2, \dots, 16$, and the product $i \cdot j$ is written in the square in row $i$, column $j$. Several rows are chosen (at least $2$) and also several columns (at least $2$). Then the numbers at their intersections are deleted.
a) Can the sum of all deleted numbers be a prime?
b) What about the sum of all undeleted numbers?
a) Can the sum of all deleted numbers be a prime?
b) What about the sum of all undeleted numbers?