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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?


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
This is more of pattern-matching than actual mathematics, I think... – J. M. Oct 13 '11 at 4:50
I'd be surprised if there was a mathematical theory behind solving IQ tests. – josh Oct 13 '11 at 4:51
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
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. – Christian Blatter Oct 13 '11 at 8:09

While one might use mathematical thought to invent justifications about what symbol comes next, the major component of this puzzle is human perception. The viewer is the one who decides what features are important, and what things are meaningful.

You can contrast this type of puzzle with something like Sudoku, which really does reduce to a deterministic mathematical study. There isn't (supposed to be) any ambiguity about what comes next in those puzzles.

Pattern recognition is certainly important in mathematics, but actually I think it is more primitive because it relates to our perception and learning process. This indicates that you will get better, more interesting answers about solving such questions if you ask psychologists and/or machine learning experts.

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Its called Raven's Progressives Matrices, in case anyone else comes across this page and wants to know what its called.

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The last one with the 3x3 grid is you add the first box to the second box to get the third box.

The one above it is everything is rotating to the right.

The one above that is when the first picture is layered on top of the one next to it any lines that cover each other disappear. Those are my fav.

The one above that is answer number 2 because there are 3 circles and 3 triangles there must be 3 of the other, and the lines in each of the three pictures are all angled the same so the last one must have the line that's missing.

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