Number sequences and IQ: discussion + problems to solve

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Postby Dubravsky » Sat Sep 17, 2011 12:34 pm

5.) First term is given. To get a next term, add eleven to the previous term and concatenate the previous term with this sum. This yields 112123112134 as an answer.

6.) To get the differences you subtract last digit from the first digit (this is an incorrect but concise explanation - digits cannot be subtracted, numbers can). In 8, both last and first digits are 8 so we get zero.

If you want to exercise the creative side of your intellect, make up your own sequences and post them here.
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Postby tvelection » Mon Sep 26, 2011 7:39 pm

Dubravsky,

I finally have some internet access so I'd like to catch up. You wanted me to try creating some number series. First, let me say that you are probably way better than this than I am ---so I apologize ahead of time if they are too easy or contrived and difficult. Anyone can write a series based on a complex algebraic procedure but the key here, I suppose, is to make them solvable more than enigmatic. A key being how many examples do you give so that it does not become obvious but there are enough to catch the sense.

One more thing, I believe in specialization of intelligence so that these problems don't, imo, necessarily result in an overall intelligence IQ as much as an analytic thinking "AQ." I mean, if someone answered a few that you could not, would you think that they were more intelligent than you ---or just better at number series analysis? Some are artistic genius' others are mathematic, others emotional, etc. In community college I had known a very intelligent woman that was extremely bright and observant and yet she needed me to help her with advanced algebra before she went into pre-calc. I'm not in any position to teach math; I just helped. And she could barely manage the manipulations. My point is she was deeply perceptive yet could not abstract procedural concepts or evaluate an equation. I'm not sure these number series problems would have accurately measured her intelligence, a genius in my estimation. She'd look at these problems and say, "huh?" But she could argue and decypher people's thoughts and motives like some virtual mind reader.

Anyway, here are two to start with: (and there may be alternate answers, I don't know for sure)

#1) 3, 5, 9, 17, ?

#2) 1, 3, 6, 9, 12, 15, ?
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Postby tvelection » Tue Oct 04, 2011 1:46 pm

#1) 3, 5, 9, 17, ?

#2) 1, 3, 6, 9, 12, 15, ?


Here are the solutions and rules.

#1) is x-1+x to produce each consecutive number.

#2) I tried to produce an early anomaly 1 to 3 that did not fit with the rest of the obvious x+3. This might be a bad idea because it renders the rule inconsistent that is these three lines added vertically:

123456 . . .
012345 . . .
001234 . . .

1369 . . .
It's interesting how difficult it can be creating the number series as oppsed to solving it. Straight simple math functions are obvious and recognizable (squares, one constant addition or subtraction, etc.) At the same time the creator of the problem realizes that this is not to be enigmatic rules of encryption but solvable. Finally, there's a consideration of how many examples are sufficient.
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Postby Dubravsky » Sat Oct 08, 2011 7:10 am

tvelection,

Firstly, I apologize for not responding for a long time. When I was first notified by email of your answer I didn't want to respond immediately, but afterwards I completely forgot about it (I started a new academic year and I had some other things on my mind...)

Your first sequence is good and easy. As for the other one, it is simply bad.

You are inputting too much arbitrary data, much more than goes out: your rule contains more information than the output. As a result no one can or no one indeed should want to reconstruct your specific generating algorithm. Look at the sequence. There is a rule generating it, that manifests itself mostly as just adding three, but manifests itself differently at the beginning. How does it manifest itself going to the question mark term? As something other than adding three? To deduce this you have only one former occurence of the other-than-plus3 manifestation, this is simply not enough to pin down precisely one rule. You can think of many rules with such a generous allowance of arbitrariness as you propose that generate the sequence. They will mostly produce 18 as an answer, but as a result it is utterly pointless to consider the sequence as anything other than multiples of three with an arbitrary 1 sticked at the beginning.

I hope I didn't discourage you from creating sequences. I will react to things you have written before sometime later, hopefully I won't forget again.
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Postby Dubravsky » Mon Oct 10, 2011 2:47 pm

To get the gist of creating these sequences you may look at the classic test SLSE I (http://www.iq-tests-for-the-high-range.com/slse.html) by Jonathan Wai, PhD. - it was a lot of inspiration for me (I gained a top first-attempt score on the test) - you'll see that it basically IS only about straight and simple math (adding&multiplying&.. small numbers), and simple concepts such as movement (shifting, permutation, ...), decomposing, grouping, alternation etc. And careful reasoning and not falling for half-baked solutions.

Concerning your earlier remarks on validity of IQ tests, you're absolutely right that intelligence is very complex, IQ tests measure how well you are able to perform on an IQ test, but scores on different tests or retests use to be quite consistent and they correlate with some real life variables. Particularly I don't think they intend to measure anything along the lines of emotional intelligence or artistic capability so don't expect them to do so.

You can quickly read on reliablity and validity on wikipedia:
http://en.wikipedia.org/wiki/Intelligen ... d_validity
http://en.wikipedia.org/wiki/Test_validity
http://en.wikipedia.org/wiki/Reliabilit ... tistics%29
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Postby phobos rising » Tue Oct 18, 2011 3:48 pm

There are no set answers for missing values in sequences. The missing
number(s) is(are) whatever the creator and/or proposer wants.

Unless the proposer states that that the sequence is arithmetic,
quadratic, exponential, or alternating two or more kinds of sequences,
for example (but not restricted to thes), then there is no set number.

Examples:


A) 1, 2, 3, __ , ...


B) 1, 2, __ , 4, ...


C) 2, 3, 6, __, ...



Possible answers to A) could be 4 or pi whatever.


Possible answers to B) could be 3 or e* or whatever


Possible answers to C) could be 18** or 11*** or whatever




* e is Euler's number, which is about 2.718


** 2(3) = 6 and 3(6) = 18


*** 2 + 1 = 3, 3 + 3 = 6, 6 + 5 = 11
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Postby Dubravsky » Tue Oct 18, 2011 4:32 pm

Hello,

You are to pick the best solution, not an arbitrary one that produces the sequence. What does "the best" mean? Firstly, let's just take it as a black box: it's just the solution the tester intends. The testee's answer in any case is a reflection of his/her cognitive processes therefore provides information to the tester. You don't even need an objective validation of the answer the way you seek it - the only important thing is that the testees' results can be statistically analyzed and this random variable can be tested for correlations with other variables (such as academic performance, income, parental IQ, etc.) and hence meaningful results can be obtained.

But after all this I'd like to impress upon you that there are pretty objective answers on the test items (at least the good ones). I know there are plenty of mathematical formulas that produce the given items, but you are to find the simplest, most fundamental and most universal solution. Read the preceding discussion for some discussion of what solutions are bad. Ok, this was still not precise: the notion could be formalized, just introduce a formal system, where you can describe the rules, and here you can correctly define what is (are) the best solutions: e.g. those rules that consider the minimal amount of data in an item randomly given (i.e., most of the data deduced), and that have the shortest description of the rule in the formal language.

While solving you almost never need to perform comparisons of rule complexity in such detail. Simply give some of the (good) tests (like Wai's SLSE I) a try and trust the items a bit, and you'll find what are these tests about. Keep in mind they are a standard tool for psychologists, appearing as subsets of many standardized tests.
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Postby phobos rising » Tue Oct 18, 2011 5:19 pm

Dubravsky wrote:Hello,

You are to pick the best solution, not an arbitrary one that produces the sequence. What does "the best" mean? Firstly, let's just take it as a black box: it's just the solution the tester intends.


There is no best solution, as that is subjective.
and what you call "arbitrary" is subjective.

No, then the tester's choice of answers is subjective. And I can come up
with missing numbers that follow similar levels of rules.

Dubravsky wrote:but you are to find the simplest, most fundamental and most universal solution.


That is still subjective. and there aren't the "most universally"
known. There are what the tester thinks are universal.

Again, the missing number questions should not be included,
unless they are testing some sort of creativity and not count
it for or against the I.Q. rating.

Dubravsky wrote:Concerning sequence creation and solving rules:

1. alternative solutions can be often thought out, but they should be always of such inferior quality that they can barely be considered solutions at all when confronted with the *intended ones.*


The "intended ones" are subjective. It is reading the mind
of the creator to some extent.**

Dubravsky wrote: This low quality of "alternative solutions" is often marked by:



b. The explanation being more complex than the *intended one*


** Again, see above.
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Postby Dubravsky » Wed Oct 19, 2011 2:12 pm

You have failed to address my principal arguments.

Even if the correct solutions are only the tester's whim, the important fact is the results can be statistically analyzed. Professional tests are regarded as having sufficient statistical validity for many purposes by psychologists. Results on these tests have been shown to correlate with variables such as academic performance, income or crime rate. There is a body of research on these topics.

To get a glimpse of why these problems do say something about certain thinking abilities, I can only advise you to try a test created by a professional, such as Xavier Jouve's or Jonathan Wai's tests.
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