MathDB

Let

n\geq 3

be a positive integer. Consider an

n\times n

square. In each cell of the square, one of the numbers from the set

M=\{1,2,\ldots,2n-1\}

is to be written. One such filling is called good if, for every index

1\leq i\leq n,

row no.

i

and column no.

i,

together, contain all the elements of

M

.
[*]Prove that there exists

n\geq 3

for which a good filling exists. [*]Prove that for

n=2017

there is no good filling of the

n\times n

square.

Problem Statement