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Curiouskid comments on Innate Mathematical Ability - Less Wrong
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That's interesting! I got the same answer but I visualized it differently. (Imagine, for each possible subpattern, i.e. "plus shape" or "dots", considering which items it appears in. In each case the answer is four, forming a rectangle. Two of the rectangles should extend into the ninth item, the one we're looking for.)
This is how I did it. My first instinct was to decompose the problem into the shapes {dots, circles, diamonds, square, +, X} and then plot which cells the shapes appear in. It's pretty easy to see the rectangles after that. Though, I didn't make the connection to XOR.