39 Responses to “IQ Test”

1. 1 1 Tristan
   March 15, 2012 at 2:20 am

   I’m no math expert, but I can tell this gonna be good.

   *settles back with popcorn

2. 2 2 Roger Schlafly
   March 15, 2012 at 2:40 am

   I got a clue by googling “Sequence problems are pointless.”

3. 3 3 Martin
   March 15, 2012 at 3:03 am

   That number is pretty close to 1/2. I’m betting it’s a instrument reading error since those are my favorite math problems.

4. 4 4 Mike H
   March 15, 2012 at 3:21 am

   Sir, you claim math created the universe. In light of integrals like these, I must ask you : who, then, created its sense of humor?

5. 5 5 Ted Levy
   March 15, 2012 at 3:31 am

   Damn! Missed it by THAT much…(holding two fingers close together)

6. 6 6 Rowan
   March 15, 2012 at 8:25 am

   Just to quibble, this is not an IQ test. ;-) In psych testing terms, an IQ test measures aptitude. This measures achievement (acquired knowledge). Or at the very least, this test requires a certain level of achievement in math before one can even begin to test the aptitude for problem solving.

7. 7 7 Boria
   March 15, 2012 at 8:33 am

   @ Rowan:
   I tend to agree with you.
   The best definition of intelligence I have seen is: The ability to adapt.
   If that is true, would not one faced with this problem do the research (adapt) in order to solve it?
   Obviously, asking a 5th grader to solve it today would not be reasonable. Asking a 1st or 2nd year college student who wants a “complete/full/well-rounded” education, to solve it by year’s end, would be reasonable.
   What say you?

8. 8 8 Ken B
   March 15, 2012 at 8:59 am

   The sequence approaches the motl ratio. Duh.

9. 9 9 Dave
   March 15, 2012 at 9:01 am

   the answer you provide equates to pi/2 which is I guess the expected result. Why expressed in that particular way for the next in the sequence (rather than any other of the infinite ways it could be expressed) is well beyond me.

   I’m just glad that it is pi/2 otherwise I will have gone crazy trying to work out why it’s a different value.

10. 10 10 nobody.really
    March 15, 2012 at 9:12 am

    Shouldn’t we have discussed this on Pi Day?

    What comes next in the following series?

    * * *

    Explanation forthcoming in a few days.

    Judging from the clues presented, I’d guess that an explanation is what comes next.

11. 11 11 Jonathan Kariv
    March 15, 2012 at 10:04 am

    The solution provided is clearly satisfies Occam’s razor…. head meet wall

12. 12 12 Sonic Charmer
    March 15, 2012 at 10:10 am

    I would think that all else equal answering anything other than pi/2 should be considered an indication of lower intelligence than answering pi/2, the most parsimonious defensible answer lacking other information (note, ‘this is a calculus problem’ does not add information).

    There may be a social-intelligence dimension here (i.e. if you need to impress someone such as a potential employer, or blog readers, you intuit that pi/2 is a ‘bad’ answer), but I don’t think that figures into IQ?

13. 13 13 martin
    March 15, 2012 at 11:05 am

    no. the answer is 34.

    starting at about 2:20 minutes.

14. 14 14 Jimbino
    March 15, 2012 at 11:08 am

    The thing that comes next is a comma. Period.

15. 15 15 Jens Fiederer
    March 15, 2012 at 11:58 am

    @martin: Good video – but you really should supply the right polynomial for 34 to fit with THIS sequence.

16. 16 16 Jimbino
    March 15, 2012 at 12:14 pm

    The eighth item in the sequence is “ice cream” and I didn’t need any calculus. I just wrote out the obvious rule for the nth item a(n):

    a(n)= (“ice cream”-π/2)*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)*(n-6)*(n-7)/(n-1)! + π/2

    and after seven half-π’s, I ended up with ice cream.

17. 17 17 Rick
    March 15, 2012 at 12:33 pm

    Well, I guess I’m smart enough to guess that what’s next is NOT that symbol over 2. Do I win?

18. 18 18 Marek
    March 15, 2012 at 1:20 pm

    Because 935615849440640907310521750000/467807924713440738696537864469=2

19. 19 19 Ken B
    March 15, 2012 at 1:32 pm

    @marek: Yes, that number is the motl limit of a sequence of 2s.

20. 20 20 Marek
    March 15, 2012 at 1:45 pm

    What’s a motl limit?

21. 21 21 James
    March 15, 2012 at 2:02 pm

    @ Boria:

    Even if you have a test to see how well one can adapt it still is about adapting over the short time period of the test.

    Possibly acquired knowledge is a measure of adaptation over several years.

    So either way it still tests a very specific intelligence.

22. 22 22 Nick J
    March 15, 2012 at 2:02 pm

    The answer is not equal to pi/2, even though it rounds it to that on the calculator when you divide, but when you subtract twice the numerator from the denominator you get a big number, so it’s more like 0.49999999999999*pi.

23. 23 23 Jonathan Kariv
    March 15, 2012 at 2:20 pm

    @ Marek: 467807924713440738696537864469 * 2 ends with an 8

24. 24 24 Jon Shea
    March 15, 2012 at 2:22 pm

    @martin, @jens:

    The unique 7th degree polynomial which evaluates to π/2 at x = {0, 1, 2, 3, 4, 5, 6} but is N at x = 7 is:

    -π(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)(x-7)/10080
    +π(x-0)(x-2)(x-3)(x-4)(x-5)(x-6)(x-7)/1440
    -π(x-0)(x-1)(x-3)(x-4)(x-5)(x-6)(x-7)/480
    +π(x-0)(x-1)(x-2)(x-4)(x-5)(x-6)(x-7)/288
    -π(x-0)(x-1)(x-2)(x-3)(x-5)(x-6)(x-7)/288
    +π(x-0)(x-1)(x-2)(x-3)(x-4)(x-6)(x-7)/480
    -π(x-0)(x-1)(x-2)(x-3)(x-4)(x-5)(x-7)/1440
    +N(x-0)(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)/5040

    You can use this technique to justify any number as being the next number in the sequence. The video argues that 2*n is a simpler explanation to the sequence {2, 4, 6, 8} since it has a lower degree than the other polynomial he uses, but I disagree. I think my answer is simpler since it can find a polynomial for any sequence, not just the one special sequence {2, 4, 6, 8}.

    This technique is called the Lagrange interpolation formula. It was used by Karl E. Linderholm to trivialize all questions of the form “What is the next number in this sequence?” in his great classic, Mathematics Made Difficult.

25. 25 25 Tim Fitzgerald
    March 15, 2012 at 3:18 pm

    Since you posed the question as an IQ test my guess at what comes next is a comma. Pretty sure that is correct.

    Tim

26. 26 26 Ken B
    March 15, 2012 at 3:56 pm

    @marek: The Motl Lemma was discussed a great deal on this blog about a year ago. Googling will turn up reams of stuff. The short answer is this: the Motl Lemma states that in any sequence which converges to 1/2 all terms are equal to 1/2. Hence that term is also equal to 1/2 and fits the pattern very well. Steve has a summary here http://www.thebigquestions.com/2011/12/30/turning-the-crank-the-year-in-review/

27. 27 27 Jimbino
    March 15, 2012 at 5:38 pm

    The original problem asked, “What comes next in the following series?”

    As I understand English, “what” does not mean “what number” and, as I understand math, the “series” is more properly called a sequence.

    Clearly my first answer: “comma” is most appropriate.

    The comment regarding calculus is ambiguous, as calculus has several different meanings, and instead of “ice cream,” I could have submitted “tartar.”

    It seems y’all are answering a question not posed, namely:

    “Assuming the missing comma to be implicit, what number most nicely follows in the given mathematical sequence.”

28. 28 28 martin
    March 15, 2012 at 5:44 pm

    @Jon Shea

    re: “I think my answer is simpler since it can find a polynomial for any sequence, not just the one special sequence {2, 4, 6, 8}.”

    if the problem is to solve many (say 1000) such problems, then yes, the general algorithm/solution that solves all problems will be simpler than the sum of all the individual algorithms/solutions.

    But, for the simple case 2,4,6,8 , 2 * n is simpler than any gereralized solution.

    if by simple we mean one of the precise definitions given in the video …

29. 29 29 MattW
    March 15, 2012 at 6:09 pm

    Whoever made the answer key is terrible at simplifying fractions. Were I a math teacher I would only give half credit.

30. 30 30 Will A
    March 15, 2012 at 8:19 pm

    I’m not looking to sec controversy or go off on a tangent but not asking a trigonometry question so close to pi day seems like a sin.

31. 31 31 Anshu
    March 16, 2012 at 12:01 am

    I followed Roger Schalafly. This is a a very Interesting example. Landsburg’s hint is kinda pointless. It is impossible for anyone to figure this out unless you noticed the sequence in your work or read about it somewhere.

32. 32 32 David Johnson
    March 16, 2012 at 4:41 am

    Just like the meaning of life the answer is 42. This is the sequence of solutions of:

    (x – 42)*(x – pi/2)^7

    Surely this is obvious?

    And you can drop the three dots Landsberg. That gives people the false impression this sequence is infinite. And you need to learn the difference between a sequence and a series.

    Tsk…

33. 33 33 Ron
    March 16, 2012 at 9:05 am

    Clearly, the answer given is not exactly pi/2. A simple two-line
    REXX program[1] gives the answer to the division as

    0.4999999999926468593249718283124405644109 (…)

    The official “answer” to the next-in-series is supplied as a
    graphic, seemingly to make it more difficult to automate the result.
    As to why this inaccurate approximation of 1/2 would be more correct
    than 1/2, I have no idea.

    [1] the program is:
    numeric digits 40
    say 467807924713440738696537864469/935615849440640907310521750000

34. 34 34 Ken B
    March 16, 2012 at 9:15 am

    @Will A: “I’m not looking to sec controversy ”
    I see no sin of it. Otherwise I’d cosh you on the head. Assuming I cot you.

35. 35 35 Bob
    March 17, 2012 at 2:16 am

    As was said, this is not an IQ test. There have been no studies showing how scores on this test correlate with those on other IQ tests or covary with general achievement or other measures of intelligence (i.e., it has not been validated). Also, the limited number of items on the test greatly reduces its utility in differentiating between various IQ levels, which is one of the primary reason for measuring intelligence. Additionally, an IQ is derived from scores on several different subtests which measure various domains (e.g., verbal skills, abstract reasoning, working memory). At best, this test would provide information relevant to one specific domain. Even then, however, a person might get this question wrong, but still score high on the construct measured by this question were other questions available to measure this construct.

36. 36 36 Ken B
    March 17, 2012 at 10:36 am

    Anyone who thought this was an IQ test failed the IQ test.
    This was an amusing teaser for a result to be named latter. Steve saw a result proing that a series of caluculus questions has a simple answer, 1/2, until a certain point and then this sudden shift to an answer amazingly close to 1/2. Steve’s post is a jesting way to highlight this remarkable result(which we do not know yet).

    Sorry to spoil the joke Steve but after my boner and neutrinos jokes I feel entitled :)

37. 37 37 improbable
    March 17, 2012 at 11:27 am

    A comma, surely.

    Then the \ldots.

    (sorry)

38. 38 38 Eliezer
    March 19, 2012 at 7:44 pm

    I plugged the numbers into excel and got pi/2, but it probably rounded off somewhere.

39. 39 39 mobile
    March 20, 2012 at 12:25 pm

    It turns out that when I have Google in front of me, I have a high IQ.