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some puzzle that can be found online are typically a 3x3 grid where you've got nine spots filled with some images or symbols or geometric figures and you have to predict what the missing one should be. Some of them are made out of symbols, some other are little 3x3 grids (inside the big grid) with some number of symbols (crosses, asterisks, etc..) placed according to some pattern and, again, you have to guess what pattern the missing grid would be.

Does anyone have any reference where I can find how they can be solved, or any theory behind this kind of puzzle?

EXAMPLES:

Bergman's IQ test

IQ test

IQ test

IQ test

Again, I am not looking to the specific solution of the examples above. I'd like to have a theory behind it, or tips to solve them.

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It would be incredibly helpful if you could include an example of such a puzzle... – Zev Chonoles♦ Oct 13 '11 at 4:03
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This is more of pattern-matching than actual mathematics, I think... – J. M. Oct 13 '11 at 4:50
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I'd be surprised if there was a mathematical theory behind solving IQ tests. – josh Oct 13 '11 at 4:51
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Someone should make a deliberately fake IQ test with complicated RNG-seeded 'patterns' and send it to MENSA or another society, then publish the results. Done sufficiently cleverly I imagine it could be another Sokal-type affair. // Also, I likewise doubt if there's any purely mathematical theory behind these. You'd have better luck in communities devoted to cognition or machine learning. – anon Oct 13 '11 at 5:10

1 Answer

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This is what mathematics is all about: You observe a more or less complex pattern and try to find the rule that generates this pattern. Such a rule is called a theorem.

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