MathDB

On a

30\times 30

board both rows

1

30

and columns are numbered, in addition, to each box is assigned the number

ij

, where the box is in row

i

and column

j

N

columns and

m

rows are chosen, where

1 <n

and

m <30

, and the cells that are simultaneously in any of the rows and in any of the selected columns are painted blue. They paint the others red . (a) Prove that the sum of the numbers in the blue boxes cannot be prime. (b) Can the sum of the numbers in the red cells be prime?

Problem Statement