[hughprime]

Those sorts of questions always bothered me in IQ tests too. I was also always bothered by questions like:

"What comes next in this sequence? 1,4,9,16,25,"

Sure, the answer might be 36, but then again maybe we're looking at some subtler sequence of numbers than that. Maybe it's "the number of bald men who walked past my house every hour since 5am". Maybe the next number is 345 due to the annual Patrick Stewart Lookalike Parade. Who knows?

[mattmaroon]

You're probably taking it too seriously then. There's a certain subtext, the catching on to of which might be part of the test, that it's a rational and discernible pattern, and that if the answer is not 36 then the question is broken.

[hughprime]

You're probably taking it too seriously then.

Oh, certainly. I've never found a case where there's genuine ambiguity, it's just that there's a certain part of my brain which takes delight in pointing out all the potential flaws in everything I read. It's much harder to concentrate on the test when half my brain is busy visualizing what four hundred Captain Picards would look like marching down my street.

[amix]

I am no fan of IQ tests myself, but I think in most tests they are looking for the most simple and logical answers - and they are trying to create tests that have very little ambiguity. In your sequence it's more logical and simple that the answer is 36, than it is how many bald men walked by your house today.

I don't know if IQ tests tell anything about a person's real intelligence, but I think that most intelligent people can become very good at solving these tests.

[der_ketzer]

There's a very good movie "The Oxford Murders", where the math professor talks about that. Every sequence has many answers, the trick is to find how to build the sequence you want and when you achieve thar, your answer is as correct as the "right answer".

[hc]

the answer is the simplest possible answer. this isn't obviously well defined, but it can be made so in at least one way: http://en.wikipedia.org/wiki/Kolmogorov_complexity

[jerf]

No dice. Kolmogorov complexity is critically dependent on the encoding scheme you use for the complexity measure, and given the nature of the problems in question that's going to really not work. If your encoding scheme favors polynomials but makes expression squares a royal pain, you're going to get a radically different K-complexity number than you will if your encoding goes the other way around. And coming up with both such encodings is trivial.

This is why proofs using K-complexity (forgive me, I often misspell it) always use it in a way that doesn't involve actually assigning numbers to the K-complexity; while it has certain desirable properties, there is no unique K-complexity value for a given language.

Aaaaand it's exactly this reason I also loathe those questions. It is much less "do this mathematical thing" than "read the puzzle-maker's mind", and quite frequently there is simply literally not enough information in the sequence to read the puzzle-makers mind. With an uncountably infinite number of functions to choose from and a finite set of inputs to choose among them, it's a complete joke of a test. On the other hand, with suitable constraints given in advance it could prove quite useful. (... but that would remove the thrill of lording the answer over people, methinks, which I think is a distressingly large part of such problem's appeal....)