Corresponding squares 2

 Ok, I simplified the method of Zinar a bit.

Take two squares that are diagonally adjacent on the shortest route from invasion square to invasion square. Choose the square that makes a triangle. That can be c4, d3 or f3. That doesn't matter (I haven't checked that yet). Let's take d3. Put a 5 on it. That is the middle of a 3 x 3 square.

White to move

7k/1p6/1P2p3/1P2P3/4P1p1/6P1/8/K7 w - - 0 1 

Put the digits 1 to 9 around it.

White to move

Let's extend that as follows. 2, 5, 8 is repeated to the left. Then 1, 4, 7 is repeated to the left:

Then do the same downwards:

White to move

Then do the same with blue.

White to move