MathDB

Let

A

and

B

be two

n \times n

square arrays. The cells of

A

are labelled by the numbers from

1

n^2

from left to right starting from the top row, whereas the cells of

B

are labelled by the numbers from

1

n^2

along rising north-easterly diagonals starting with the upper left-hand corner. Stack the array

B

on top of the array

A

. If two overlapping cells have the same number, they are coloured red. Determine those

n

for which there is at least one red cell other than the cells at top left corner, bottom right corner and the centre (when

n

is odd). Below shows the arrays for

n=4

. https://cdn.artofproblemsolving.com/attachments/8/e/cc8a435cb28420ccf91340023d440e39f0e849.png

Problem Statement