## Math sequence problems

Discussions concerned with knowledge of measurement, properties, and relations quantities, theoretical or applied.

### Math sequence problems

I am sure this are quite easy, but I've forgotten how to work out sequences.

These are both from IQ test I did recently and I got one right without attempting to work it out ...

1) 2 - 3 - 6 - 7 - 8 - 14 - 15 - 30

Which one doesn't belong in series?

2) 1 - 2 - 5 - 10 - 13 - 26 - 29 - 48

Which one doesn't belong in series?

1, 5, 26, 29 or 48?

3) 1 - 8 - 27 - x - 125 - 216

What is x?

36, 45, 46, 64 or 99?

Thanks

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### Re: Math sequence problems

Hi..

Guess? I'm a bit rushed.. but here are my answers..

1) = 14 (multiple answers but 14 violates most)
2) = 1 (growing primes with interwoven 3's)
3) = 64 (46 is too small, 99 is too large)

Regards,
Dave :^)

Ps. Do you know the correct answers?

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### Re: Math sequence problems

1) is 8, it is nothing to do with math really.

edit : Wait I may be wrong! haha!

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### Re: Math sequence problems

BadgerJelly » August 10th, 2017, 2:26 am wrote:I am sure this are quite easy, but I've forgotten how to work out sequences.

These are both from IQ test I did recently and I got one right without attempting to work it out ...

1) 2 - 3 - 6 - 7 - 8 - 14 - 15 - 30

Which one doesn't belong in series?

8 does not belong.
The pattern is... add one to get the next number then double this number to get the next.

BadgerJelly » August 10th, 2017, 2:26 am wrote:2) 1 - 2 - 5 - 10 - 13 - 26 - 29 - 48

Which one doesn't belong in series?

48 does not belong
The patter is... double to get the next number then add three to that number to get the one after.
The next one in the series should be 58 not 48.

1, 5, 26, 29 or 48?

BadgerJelly » August 10th, 2017, 2:26 am wrote:3) 1 - 8 - 27 - x - 125 - 216

What is x?

64
These are just the cubes of 1, 2, 3, 4, 5, 6, ....

All three took me about five minutes altogether.

mitchellmckain
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### Re: Math sequence problems

Same here, a couple minutes for first and second series.

The last one I just knew as soon as I looked at the series.

Braininvat
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### Re: Math sequence problems

And then there's the infamous...

4, 8, 15, 16, 23, 42

(don't worry, there's no algorithm for this set of numbers)

If you never watched the ABC series "Lost," then this doesn't mean anything. Fans may have noticed that two of the numbers form the flight number of the jet that crashed. And that the last is Douglas Adams meaning of life. And that summing the set yields 108, which can also be expressed as "one to the first times two to the second times three to the third."

Braininvat
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### Re: Math sequence problems

Dear,

These are both from IQ test I did recently and I got one right without attempting to work it out ...

proposition : IQ tests all miss the point.

1) 2 - 3 - 6 - 7 - 8 - 14 - 15 - 30

Which one doesn't belong in series?

8, because it is the only non-Mobius number.
2=2^1
3=3^1
6=2^1 3^1
...
30=2 x 5 x 3

2) 1 - 2 - 5 - 10 - 13 - 26 - 29 - 48

Which one doesn't belong in series?

1, 5, 26, 29 or 48?

idem, 48=2^4 3

henriette
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### Re: Math sequence problems

henriette » February 23rd, 2018, 7:11 am wrote:Dear,

These are both from IQ test I did recently and I got one right without attempting to work it out ...

proposition : IQ tests all miss the point.

1) 2 - 3 - 6 - 7 - 8 - 14 - 15 - 30

Which one doesn't belong in series?

8, because it is the only non-Mobius number.
2=2^1
3=3^1
6=2^1 3^1
...
30=2 x 5 x 3

But 5 is a mobius number and is not included, as well as 10, 11, 13, 17, 19, 21, 22, 23, 26, and 29. Therefore this reasoning seems specious to me. It is like saying 8 doesn't belong because the rest are non-cubes -- ignoring the fact that both 4 and 5 are non-cubes also but not included.

henriette » February 23rd, 2018, 7:11 am wrote:
2) 1 - 2 - 5 - 10 - 13 - 26 - 29 - 48

Which one doesn't belong in series?

1, 5, 26, 29 or 48?

idem, 48=2^4 3

It is true that the correct number 58 = 2 x 29 is also mobius, but it still seems a bit concidental.

I seems to me the sequence could easily have been
2 - 4 - 7 - 14 - 17 - 34 - 37 - 64
to which your reasoning would have failed because both 4 and 64 are non-mobius.

If you make these IQ question such that you can leave out valid members then I suspect they would become ambiguous because you could make equally valid arguments for different possible answers.

mitchellmckain
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### Re: Math sequence problems

Braininvat » August 10th, 2017, 3:55 pm wrote:
4, 8, 15, 16, 23, 42

(don't worry, there's no algorithm for this set of numbers)

There's an algorithm for every finite sequence. The algorithm for this particular sequence is:

Print 4
Print 8
Print 15
Print 16
Print 23
Print 42
Halt

Turing would approve.

I do take your point that there are sequences whose generating principle is social as opposed to mathematical. For example there's the famous sequence: 4, 14, 23, 34, 42, 50, 59, ... These are the northbound numbered stops of Manhattan's A train.

henriette » February 23rd, 2018, 6:11 am wrote:proposition : IQ tests all miss the point.

Absolutely. In his famous and witty pamphlet, Mathematics Made Difficult, Carl Linderholm makes this exact same point.

Any finite sequence can be fitted to a Lagrange interpolation polynomial. Since a polynomial is one of the simplest and most common mathematical functions, Linderholm points out that that any number whatsoever is a correct response to any of these kinds of puzzles.

These questions don't test for mathematical ability; but rather for the ability to determine what the examiners think the right answer should be. They're testing for conformance and lack of creativity.

Even these "what number doesn't belong" are the same. All numbers belong and all numbers don't belong for a wide variety of interesting and uninteresting reasons.
someguy1
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### Re: Math sequence problems

someguy1 » February 24th, 2018, 9:59 pm wrote:These questions don't test for mathematical ability; but rather for the ability to determine what the examiners think the right answer should be. They're testing for conformance and lack of creativity.

Even these "what number doesn't belong" are the same. All numbers belong and all numbers don't belong for a wide variety of interesting and uninteresting reasons.

Even though I criticized henriette's response, I don't entirely disagree with this. On the other hand, it is not supposed to be about mathematical ability. It is about searching for possible explanations and picking the one which fits best. But it is quite true that someone may very well look for explanations in an entirely different direction, especially if they have an expertise in a particular area which may lure them into looking in such a direction. Then the question would not measure IQ accurately in their case.

Another test which can be greatly misled by imagination and particular interest is the Rorschach test. Use this on a child who spends all his time reading sci-fi and thinking about such things and the sociologist doing the test might think they are crazy. (P.S. this actually happened to me, though actually talking with a psychiatrist dispensed with this test result quite conclusively)

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