It was the average of the min and max. I figured that by subtracting this amount, some positive and negative numbers might pop out in an obvious looking manner. It also has the advantage of changing the sum obtained from 63 to 3 (63-4*15=3), which is a bit easier to work with (I have a touch of dyscalculia, and try to simplify things to single digit operations when I have to do mental arithmetic). Subtracting 16 would have been my next thought, as that would have changed the sum to -1, which is also easy enough to work with.
From there, one can simplify further: reduce the problem to 4×4 blocks, figure out what is going on, increase the block size and repeat.

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