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Number Sequence Problem. Solution? Number Sequence Problem. Solution?

05-30-2010 , 06:02 PM
i'm suggesting that eating shampoo interferes with your ability to detect patterns in a series of numbers.
Number Sequence Problem. Solution? Quote
05-30-2010 , 06:28 PM
can anyone figure out what the next number in this series is?
2 4 8 15 16 23 ?
Number Sequence Problem. Solution? Quote
05-30-2010 , 07:37 PM
Quote:
Originally Posted by shmoygens
can anyone figure out what the next number in this series is?
2 4 8 15 16 23 ?
Did you mean: 4 8 15 16 23 42
Number Sequence Problem. Solution? Quote
05-30-2010 , 09:46 PM
Black Smoke is the next number...then a show that makes no sense and I'm glad is over
Number Sequence Problem. Solution? Quote
05-31-2015 , 03:02 AM
I’d like to add my two cents.

1. Often, in a numerical series or even in a proper IQ test, there may not be a single correct answer. There may be only one. Or there may be more than one.

2. Answers are almost never as important as the reasoning and logic behind the answer. There can be many ways to solve a question and all of them may be correct. But often they may lead to different solutions, and it is the reasoning that is more important and needs to be sound. This is a complicated concept and I don’t have the time to explain the whole thing.

3. I have gone through this series and I confirm that 150 is the incorrect answer. And even if there is a way to reach that answer, I can guarantee you that it isn’t the only solution.

4. I have found at least two other correct solutions to this problem. Both of which are simple and direct. Neither requires advanced mathematics knowledge. Both solutions are fit for an IQ test answer.

5. And both these solutions have already been posted in the thread at physicsforum. The better one is 126. And the other one is 118. It depends on the method you use to solve the series. Both are correct.

6. I’ll solve one of the above, 126 that is.

7. Here you go:

3 8 18 30 70

Add the consecutive numbers.

11 26 48 100

Again add the consecutive numbers.

37 74 148

Now. When there are only 3 numbers in a sequence, you are NOT allowed to take their differences to compute the fourth number. However, you are supposed to form a chain of numbers without considering their differences or the like. The reason is pretty obvious but difficult and lengthy to explain. Also, this doesn’t hold when at least 4 numbers are present. And of course, if you only have 2 numbers in a series, then it isn’t a series so there is no third number as it could be anything.

Now:

1 x 37 = 37
2 x 37 = 74
4 x 37 = 148
8 x 37 = 296 is the obvious solution over here.

296 – 100 = 196

196 – 70 = 126 = The most obvious and simple answer that somebody had already pointed out previously.

8. If you need to go into advanced concepts like polynomials, then you have flunked the IQ test. IQ tests measure simplicity, beauty and native intelligence. Not knowledge. Although many scientists make tests that depend on knowledge, they are absolutely futile unless everybody has all aspects of the required knowledge. I do not come from that school of thinking and believe in simple concepts that are driven by common sense alone.

9. Just because somebody, some website or some book labels XYZ as the answer, it doesn’t make that correct. And it doesn’t imply that there can be no other solution(s), that are comparable or better or at least correct.

10. Chances are a single line of thinking devised a question. That however doesn’t imply that no other method of reverse engineering the answer is correct. Everything is relative and bound by reasoning and reasoning alone.

Thank You so much!

God Bless

Aakshey
Number Sequence Problem. Solution? Quote
06-01-2015 , 09:14 PM
Quote:
Originally Posted by EjackulEight
I did an IQ test today, in it was a number sequence problem which I simply just cannot work out the answer to - and has been grating my mind all day.

3, 8, 18, 30, 70, ?,

I really can't see the solution to it, maybe a fresh pair of eyes will see it.
Well the easy stupid answer is to see this as 2 sets of 3 numbers the first set 3,8,18 that looks like the difference doubles 3+5=8 then 8+10=18

If you do the same for the second set of 3

30 +40 =70

so the next must be 70+80 (=2*40) =150


But this is so ridiculous arbitrary yet simple but who decided the rules are to break in 2 sets of 3 each.
Number Sequence Problem. Solution? Quote
06-01-2015 , 10:12 PM
The sequence of numbers does not appear in the Sloane Encyclopaedia of Integer Sequences so I strongly suspect a typo in the problem or in the OP.
Number Sequence Problem. Solution? Quote
06-02-2015 , 02:01 AM
I gave the problem to my school-age daughter (before realizing how "problematic" this problem really is). After fiddling for quite awhile, she came up with 142. I asked her how she got that answer.

Paraphrasing, she said the Kth number in the sequence is the sum of all the previous numbers in the sequence with an additional summand of the Kth odd number greater than one, except if the Kth odd number greater than one is composite (not prime), then this summand just becomes one.

3=(0)+(3)
8=(3)+(5)
18=(3+8)+(7)
30=(3+8+18)+(9)-(9)+(1)
70=(3+8+18+30)+(11)
142=(3+8+18+30+70)+(13)

When she asked if that was the correct answer, I said I did not know but that her answer was better than anything I could come up with!
Number Sequence Problem. Solution? Quote
06-02-2015 , 02:13 AM
Whosnext how old is your daughter? She must have astronomical IQ and see next my re-edited post of why i criticized the IQ test for exactly that same reason.

--
Notice however that in most IQ tests you are given some answers and have to select one so i guess the 150 was there as an answer. I can then imagine that after looking for patterns and not seeing anything basic with the other choices, the 150 seems reasonable exit and the fact that the 4th number appears disconnected from the 3 first, is the first hint this is 3 and 3 back to back 2 separate sets of sequences. OP should have given us upfront all the choices offered to produce that suggestive clue for the brain. In that sense 4 and 5 are arbitrary too provided n5>n4 at least, n6 would always have to be n5+2(n5-n4)=3n5-2n4. If n5<n4 then looking for n6 lower number using the above idea, even negative sometimes.

I guess its only reasonable within an IQ test mentality if the idea that describes the pattern, arbitrary as it is, at least appears to be simple enough so the IQ tests seeks how fast you arrive at the simple pattern. Although it still is arbitrary, its probably the simplest of all easy arbitrary ones. But then how do you decide one that didnt find it is less intelligent if that person was able in the first place to have imagined all kinds of more complex sequences using all 6 numbers and never breaking in sets of 3+3.

One brain thinks outside the box of standard 1 set logic 6th number and goes to 123 then 123 logic. That is an advantage of that brain. But the advantage of the other brain that checked even more sequences of 6 numbers is never registered as excess intelligence. So the IQ test fails somewhat.


Here is another test i saw recently that is both IQ and personality that may be telling of how different certain brains are.

I think there was some cards shown like this ;

4 squares (depicted as [] here) that were first 2 numbers and then 2 color faces.

[13],[8], [blue], [red]

The question was if told that a rule exists that back of each blue colored card there is an even number, how many card(s) do we need to turn to verify the rule?
Number Sequence Problem. Solution? Quote
06-02-2015 , 07:42 AM
doesn't make sense to me. guess i fail on 'intelligence quotient' i always thought that these tests can be studied and i don't have answer except for same as first guy who answered
Number Sequence Problem. Solution? Quote
06-02-2015 , 10:14 AM
Quote:
Originally Posted by Enrique
The sequence of numbers does not appear in the Sloane Encyclopaedia of Integer Sequences so I strongly suspect a typo in the problem or in the OP.
Many arbitrary but reasonable sequences wont appear here; x, 2x+1, 3x+2
Number Sequence Problem. Solution? Quote
06-03-2015 , 11:26 PM
3 = 1 x 5 - 2
8 = 2 x 5 - 2
18 = 4 x 5 - 2
30 = 8 x 5 - 10
70 = 16 x 5 - 10
therefore the next number is
150 = 32 x 5 - 10 and the one after is
270 = 64 x 5 - 50
Number Sequence Problem. Solution? Quote
06-04-2015 , 12:55 AM
Quote:
Originally Posted by Hired Goons2
3 = 1 x 5 - 2
8 = 2 x 5 - 2
18 = 4 x 5 - 2
30 = 8 x 5 - 10
70 = 16 x 5 - 10
therefore the next number is
150 = 32 x 5 - 10 and the one after is
270 = 64 x 5 - 50
what's the reasoning for final term getting multiplied by 5 every 4th term?
Number Sequence Problem. Solution? Quote
06-04-2015 , 12:36 PM
Quote:
Originally Posted by masque de Z
The question was if told that a rule exists that back of each blue colored card there is an even number, how many card(s) do we need to turn to verify the rule?
2. You need to verify the blue has even and the odd number is not blue.

PS: I can't come up with a solution for OP's question without involving some arbitrarily strange rules.
Number Sequence Problem. Solution? Quote
06-04-2015 , 07:54 PM
Here is another one to piss off IQ testers lol;

try the rule

a(n)=2*a(n-2)+4*a(n-3)+2 , n>3

then indeed
2*8+4*3+2=16+12+2=30
2*18+4*8+2=36+32+2=70

So the next would be 2*30+4*18+2=60+72+2=134

similar rules a(n)=3*a(n-1)-2*a(n-2) , n>2

a(n)=4*a(n-2)-2 n>3

a(n)=5*a(n-2)-2*a(n-3)-4

a(n)=6*a(n-2)-4*a(n-3)-6

None leads to 150 though. But if 150 is not given as answer then some are legitimate choices.
Number Sequence Problem. Solution? Quote
06-04-2015 , 08:43 PM
Quote:
Originally Posted by Hired Goons2
3 = 1 x 5 - 2
8 = 2 x 5 - 2
18 = 4 x 5 - 2
30 = 8 x 5 - 10
70 = 16 x 5 - 10
therefore the next number is
150 = 32 x 5 - 10 and the one after is
270 = 64 x 5 - 50
Quote:
Originally Posted by gaming_mouse
what's the reasoning for final term getting multiplied by 5 every 4th term?
because it fits
Number Sequence Problem. Solution? Quote
06-05-2015 , 03:45 PM
Quote:
Originally Posted by Hired Goons2
because it fits
based on the 2 and 10 (the only samples we have) so does adding 8, or adding the cube of the current term, or.....
Number Sequence Problem. Solution? Quote
06-05-2015 , 07:35 PM
Quote:
Originally Posted by gaming_mouse
based on the 2 and 10 (the only samples we have) so does adding 8, or adding the cube of the current term, or.....
I see that it could be -18 instead of -50 for the 7th term--I'm not seeing the "cube of the current term"
Number Sequence Problem. Solution? Quote
06-07-2015 , 10:16 PM
Quote:
Originally Posted by Hired Goons2
I see that it could be -18 instead of -50 for the 7th term--I'm not seeing the "cube of the current term"
all you are looking for is a function f such that f(2) = 10. there are infinitely many of them.

you arbitrarily chose f(x) = x*5. i was pointing out that f(x) = x + 8 and f(x) = x + x^3 also work. because of the kind of test it is, you have a reasonable expectation that the "correct" answer is not something too crazy, that it's something that "makes sense" or "seems right." but even with this fuzzy constraint, i see no reason to prefer "x*5" over "x+8" and you can surely come up with other reasonable candidates.
Number Sequence Problem. Solution? Quote
06-16-2015 , 11:19 AM
it's a reach, but it creates the sequence 3, 8, 18, 30, 70, 150.

f(x) = (360 -1722x + 4225x^2 - 2435x^3 + 575x^4 - 43x^5)/120
f(0) = 3, f(1) = 8, f(2) = 18, f(3) = 30, f(4) = 70, f(5) = 150
Number Sequence Problem. Solution? Quote
06-17-2015 , 09:57 AM
You could come up with a fifth degree polynomial that has f(0) = 3, f(1) = 8, f(2) = 18, f(3) = 30, f(4) = 70 and f(5) = whatever you want.
Number Sequence Problem. Solution? Quote
06-17-2015 , 03:53 PM
(its lengthy but read it to see if something interesting emerges here as a paradigm in artificial intelligence)

Ok lets change the thread to try to find any function or recursive relationship that uses as little as possible input to derive the remaining terms and 150. Take that to mean use all but 150 and predict 150 or use only the first 1,2,3 and predict all rest etc.

We can ask for example if there is any polynomial that has less than 5 parameters that produces all 6 terms. The above 5th degree has 6 parameters so it cant count (i had found it also before but didn't post because of the reason Enrique criticized it ie 150 is not predicted, just demanded to fit it) .


I did a recursive analysis of the type of linear connection between any prior terms and i posted some results some time ago.

I didnt try nonlinear recursive search and i didnt try a higher than 5th degree polynomial search that uses only 5 parameters and predicted 150 etc. But there may exist one because you have effectively turned the degree into a parameter and the ways to choose any 5 or less of possible power terms less than some maximum into another "parameter" lol and the numbers are integers so we may get lucky. Eg one might be able to find an 8th degree that uses the 8th, 5th, 3rd, 2nd and 0th terms as parameters etc.

Of course the simpler of these will be a decent candidate finally.

Naturally this has nothing to do with original "IQ test" that was likely wanting to see the 6 in groups of 3 and 3 as in 3,8,18 and then 30, 70 150, especially if the IQ test had multiple choices and 150 was there. Its just a challenge to find the simpler possible answer in order to mock the IQ test itself, especially if there proves possible to find such "easy" in the final expression/rule relationship.

This of course is impossible to guess in few minutes even if you are very smart anyway but a computer might be able to still find, yielding another source of "intelligence" for example in the form of brute force or creative usage of brute force because one is not frustrated by the depth of complexity introduced due to enough memory and speed. Why go there? Possibly due to offering a new insight into what intelligence can be - in an emergent sense out of very dense number of operations conscious or unconscious ones - in line with ideas i have had before about how easy it is to produce eventually self awareness by making the density of operations of the system very substantial and playing with patterns discovered in every aspect of life, even witnessing the process itself and having our awareness prove entirely emergent. By that i mean awareness proves the observation of the function of our own brain constantly playing with patterns vindicated in prior life.

Eg you see water and all its properties instantly become available in your brain and maybe one of them fits what you need now so you go do it - eg drink it or use it to clean etc, you see tools and all combinations of prior usage of any subset of them become available through memory of past experiences so its easy to imagine novel combinations of tools by breaking them in parts and connecting them (which results in intelligent behavior but is only based on brute search of prior life connections the brain does read fast unconsciously leading to the effect of intricate intelligent "thought", the solution). Now try to imagine breaking down the sequence of intelligent actions; i get thirsty, i think of water, i look around and use sound etc (only way to search), i see (or hear or smell) kitchen (ie source of water), i stand up and go there and in each step i avoid objects, i place legs how to walk and balance, avoid accidents etc all a series of intelligent steps previously experienced but the total result may be entirely novel (eg i havent walked before in a new room in a new apartment i found myself just now, and similarly when you try to solve a math problem you havent necessarily been there before but you have used before the intermediate steps in different order or place). And this is how emergent intelligent behavior works by vast number of connections allowed to be composed fast probably enhanced by currently elevated weights placed in each one as senses and memory "read" and organize the environment and overall behavior has some action reward structure (ie purpose) motivating the emergent sequence of intelligent steps. Now you also observe all this and become amazed (= awareness).

Last edited by masque de Z; 06-17-2015 at 04:00 PM.
Number Sequence Problem. Solution? Quote

      
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