MathDB

Let

G

be the set of points

(x, y)

such that

x

and

y

are positive integers less than or equal to 6. A magic grid is an assignment of an integer to each point in

G

such that, for every square with horizontal and vertical sides and all four vertices in

G

, the sum of the integers assigned to the four vertices is the same as the corresponding sum for any other such square. A magic grid is formed so that the product of all 36 integers is the smallest possible value greater than 1. What is this product?

Problem Statement