MathDB

A number is written in each cell of the

N \times N

square. Let's call cell

C

good if in one of the cells adjacent to

C

on the side, there is a number

1

more than in

C

, and in some other of the cells adjacent to

C

on the side, there is a number

3

more than in

C

. What is the largest possible number of good cells? Proposed by A. Chebotarev

M2791