MathDB

There is a

50\times 50

grid board.. Carlos is going to write a number in each box with the following procedure. He first chooses

100

distinct numbers that we denote

f_1,f_2,f_3,…,f_{50},c_1,c_2,c_3,…,c_{50}

among which there are exactly

50

that they are rational. Then he writes in each box (

i,j)

the number

f_i \cdot c_j

(the multiplication of

f_i

c_j

). Determine the maximum number of rational numbers that the squares on the board can contain.

Problem Statement