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Kindly 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 a better answer than XOR, in a sense: it describes the pattern more narrowly. If the "true pattern" were XOR, it would be possible to have a shape or subpattern occur 6 times (if it is missing once from each row and column, e.g. if it is present everywhere except in one of the diagonals). Since this does not occur for any of the six shapes, this provides some evidence that XOR is not the "true pattern".
(Similarly, this is very strong evidence that "just have 4 of each shape" is not the true pattern: there are 126 ways to place a shape in 4 cells, and only 9 of them make a rectangle shape. The case against XOR, where we notice that only 9 of the 15 XOR patterns are used, is much weaker, but I still believe it.)
Of course, if the goal is to just solve this particular problem, then any method works. But if we were studying the appearance of many matrices with this pattern, then you would get twice as many research points as anyone else :)