[gweinberg]

The flaw with that "solution" is that if you have found the rule, you should be able to say whether a new image belong on the right or the left if it is presented to you. If you say, "I can do that, but I need one more bit of information, namely whether the new image belongs on the right or the left", that's a pretty severe defect.

[rrmm]

There's no necessity (in general) that a new image should be able to be classified under the rule. If I give you two finite groups A={1,3,9,-2} and B={7,-11,i,5} and the rule actually is tautological, Then a new number 22 doesn't belong to either group under the rule.

A few of the examples from the article actually are similar. The two circles where one circle is either clockwise or counterclockwise from the nearest indention only admits pictures with two circles, one on the surface of the other and an indentation. There are images which wouldn't fit into either.

A math professor of mine was illustrating this point with number series (of the sort on aptitude tests, eg squares,arithmetic sequences, etc), by listing an obvious sequences whose completion ended up being an obscure function which diverged at the next point.

So, the trivial solution (and the more ultra-complicated solution) is defective basically because it's not interesting under the rules of the game which assumes the answer is somehow interesting, but not impossible to guess.