MathDB

Find the maximum possible value of

n

, such that the integers

1,2,\ldots n

can be filled once each in distinct cells of a

2015\times 2015

grid and satisfies the following conditions:
[*] For all

1\le i \le n-1

, the cells with

i

and

i+1

share an edge. Cells with

1

and

n

also share an edge. In addition, no other pair of numbers share an edge. [*] If two cells with

i<j

in them share a vertex, then

\min\{j-i,n+i-j\}=2

Problem Statement