Got it. Subtracting 16 is what seemed natural to me, since 4 × 16 = 64, the magic sum in a 4 × 4 magic square. But I think the brilliance of what you did is realizing that all numbers could be changed to ones that are easier to work with. Perhaps should all have a touch of dyscalculia, if it means we’d come up with strategies like this!

]]>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.

]]>Nice strategy, Xander. But why 15? Seems subtracting any number would help… just wondering why that one.

]]>Yeah, yours was a hard one, Sue. Let me know if you think I should move it to a different category.

]]>De nada, Shaun! Yours was totally worthy of inclusion. I hope lots of folks enjoy your post.

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