Hint (this will show I've already done it!!): answer > 10,000 and < 100,000; all 5 digits even
A 6 by 6 array is filled with 6 1's and 30 0's,
such that each 1 has only 0's as immediate neighbours,
horizontally, vertically and diagonally.
As example:
1 0 1 0 1 0
0 0 0 0 0 0
1 0 1 0 1 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
In how many different ways can the array be filled?