Just a guess. Perhaps you could use the other monk's blanked out solution to create an initial grid. Then, recreate this solution in the other grids, but transform it in some simple way in order to make sure it doesn't break the rules. My shot - just a first guess - is below, hidden:
Hmm. Let's try a 2 x 2 version. The initial grid is
obviously. Now you need to fill in
Clearly, as you move across, you need to shift rows:
And as you move down, you need to shift columns:
note that the lower left grid is just the upper left grid with columns shifted along.
it turns out that the column shift from the grid above, and the row shift from the grid to the left, give identical results.
Perhaps this will work with N>2. Or not. Enjoy.
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