MathDB

In each square of a

5\times 5

board is written

1

-1

. In each step, the number of each of the

25

cells is replaced by the result of the multiplication of the numbers of all its neighboring cells. Initially we have the board of the figure. https://cdn.artofproblemsolving.com/attachments/2/d/29b8e5df29526630102ac400a3a2b2f8fee4f7.gif Show how the board looks after

2004

steps.
Clarification: Two squares are neighbors if they have a common side.

Problem Statement