MathDB

Let

n

be a positive integer. An

n \times n

matrix (a rectangular array of numbers with

n

rows and

n

columns) is said to be a platinum matrix if:
[*] the

n^2

entries are integers from

1

n

; [*] each row, each column, and the main diagonal (from the upper left corner to the lower right corner) contains each integer from

1

n

exactly once; and [*] there exists a collection of

n

entries containing each of the numbers from

1

n

, such that no two entries lie on the same row or column, and none of which lie on the main diagonal of the matrix.
Determine all values of

n

for which there exists an

n \times n

platinum matrix.

Problem Statement