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slicko comments on Innate Mathematical Ability - Less Wrong
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How fancy? I solved it by thinking in terms of “canceling each other out”. So if a small circle is in cell 1 and cell 2 of a row, they cancel each other out and don't appear in cell 3, but if the circle is only in cell 1 or cell 2, it is preserved. The intuition of canceling each other out is taught to children as early as they're taught fractions: (2*3)/(3*5) = 2/5, because if 3 is both in numerator and denominator, you cross it out. This doesn't require knowing anything about logical operators.
I had the same reaction to calling it "fancy".
I got the answer fairly quick (didn't time it, but probably about a minute or two). In my head, I was thinking of subtraction, not even "cancelling out".
In a row, cell 1 minus cell 2 equaled cell 3.
I suppose that is an XOR pattern after all, but you only need knowledge of basic arithmetic to verbalize the pattern.
(edit: upon rereading my answer, I guess it's not fair to call it a subtraction only, since I'm still keeping around shapes from cell 1 or cell 2 provided they weren't subtracted. Apparently my brain is doing XOR while thinking of it as a subtraction)