Number sequence: 83 80 84 83 88 95 ....

[dirk_mec1]

Homework Statement

Fill in the dots:

83 80 84 83 88 95 ...

Pick one of the following answers: 95 91 83 87

Homework Equations

The Attempt at a Solution

84-83 = 1
88-84= 4
88 + 7 = 95 ?

 

[jedishrfu]

Can you provide some context here:

What course are you taking?

What book are you using?

What sequences have you learned about?

I don't see an obvious arithmetic pattern to the numbers.

Have you tried to make a case of pros and cons for each of the possible answers?

 

[dirk_mec1]

I find it hard to find pro's and cos for each answer. I've learned a large number of sequences yet I cannot figure this one out.

Most other sequences were about linear/multplicative differences (or differences of differences) or using subsequences but they were not hard. This sequence is amidst those so the solution must not be hard to find.

 

[jedishrfu]

Starting with Pick one of the following answers: 95 91 83 87

95 pro its one of the numbers in the list, con there's no case of repeated numbers next to each other in the sequence
91 pro its not in the list, con its -4 from the last number of the sequence
83 ...
87 ...

 

[dirk_mec1]

83 ... pro it repeats but other than that there is no good reason to pick it
87 no clue.

 

[jedishrfu]

Where did you find this problem?

 

[berkeman]

Where did you find this problem?

Good question. Does not appear to be ASCII or some other similar encoding. I know which answer I would pick, but it still has the con that it doesn't fit any simple pattern, and relies on an assumption about the overall pattern...

 

[dirk_mec1]

Good question. Does not appear to be ASCII or some other similar encoding. I know which answer I would pick, but it still has the con that it doesn't fit any simple pattern, and relies on an assumption about the overall pattern...

Please explain as I am clueless.

 

[berkeman]

Please explain as I am clueless.

Explain which part?

 

[jedishrfu]

Sometimes number sequences aren’t based on an arithmetic or geometric progression. They instead might be character codes like ASCII or Unicode and when converted to characters display a message. Or they could be some well known number like pi broken up into smaller two digit numbers, 31 41 59 26 ...

So if your sequence is from a math book it may be an arithmetic or geometric sequence. If it was from a puzzle book then it might be some more fanciful scheme.

 

[dirk_mec1]

Explain which part?

What you would pick and why.

 

[dirk_mec1]

Sometimes number sequences aren’t based on an arithmetic or geometric progression. They instead might be character codes like ASCII or Unicode and when converted to characters display a message. Or they could be some well known number like pi broken up into smaller two digit numbers, 31 41 59 26 ...

So if your sequence is from a math book it may be an arithmetic or geometric sequence. If it was from a puzzle book then it might be some more fanciful scheme.

Like I said it was in a series of other much simpler sequences therefore I would not expect anything out of the ordinary.

 

[berkeman]

Like I said it was in a series of other much simpler sequences therefore I would not expect anything out of the ordinary.

Can you tell us where these series were? It would help us to know that.

What you would pick and why.

I'm happy to, but I'd like to see the source first.

 

[jedishrfu]

Yes, I've been asking that same question: Where did you find this sequence? and what math are you studying?

 

[Ray Vickson]

Like I said it was in a series of other much simpler sequences therefore I would not expect anything out of the ordinary.

People keep asking you, and for some reason you keep refusing to answer. Is the problem from a book? If so, which book? Is this part of a course, or is it just "recreational math"?

 

[dirk_mec1]

People keep asking you, and for some reason you keep refusing to answer. Is the problem from a book? If so, which book? Is this part of a course, or is it just "recreational math"?

Answers:
1) no
2) no
3) Yes, from a basic iq test.

 

[Fewmet]

A favorite puzzle of mine starts with this:
A E F
B D G
C
and asks where the H belongs.

Spoiler: Where the H belongs

The top line. All top line letters are made with only straight lines. All second line letters are made with straight and curved lines. All bottom line letters are made only with curved lines.

Applying the same kind of reasoning as that one requires and the recurrence of the 83, I can offer an argument for the the next number in dirk_mec1's posted problem being 83. I wish it were more more compelling, but it is the best I have found so far.

 

[Fewmet]

Rts: the spaces in the letter puzzle disappeared when it posted. It should loo like this:

Right after posting, I found another line of reasoning for 83 being next that is a little more compelling.

 

[LCKurtz]

When I was in maybe the 7th grade, what we called Junior High back in the stone age, everyone had to take an IQ test, the results of which we were not supposed to be able to learn until sometime after we graduated. I remember being very frustrated with that test, so much so that I vowed I would never go seek the results. And I never did. One question that sticks in my mind from that test was:
Which two are the most similar of: A cannonball, a pencil, a key? I can loosely defend more than one answer to that ridiculous question and the whole test was somewhat like that. I thought at the time that divining a person's IQ with questions like that was nonsense and I still think so. The question in this thread strikes me as a waste of time for similar reasons.

 

[Fewmet]

Which two are the most similar of: A cannonball, a pencil, a key? I can loosely defend more than one answer to that ridiculous question and the whole test was somewhat like that.

I can see assessment value in something like that is the task is to see how answers you can generate with convincing rationales. That, of course, is not the case here.

The question in this thread strikes me as a waste of time for similar reasons.

I have been following the thread (and working on the puzzle) in hopes that there is a clever, satisfying answer. I would feel really pleased with myself if I found it. I begin to suspect my hopes might be dashed...

 

[jedishrfu]

Yeah these tests reminded me of English class. Now students underline the gerund in the sentence below.

And I underlined the “ger” in one word and “und” in another. Wrong!

 

[Delta2]

I would go for 83 , cause its the only pattern I can spot (83 followed by two numbers, then 83 again followed by another two seemingly random numbers,...)...

 

[mathwonk]

lagrange's interpolation formula anyone? (i.e. you can find a (unique) polynomial f(n) of degree ≤ 6 that will give you these 6 numbers for n = 1,...6, and as next number f(7) = any result you want.)

e.g. [(x-1)(x-2)...(x-6)]/[(7-1)(7-2)...(7-6)] equals 1 at x=7 and equals zero at x=1,...6. doing this for each number 1,...7, we can multiply each term by what ever we want, add the results, and get a polynomial that has arbitrary values at x=1,...,7. i.e. just as a linear functionn can pass through any two points with distinct x - coordinates, so also can a 6th degee polynomial pass throug any 7 such points.

So if you are trying to come up with a polynomial rule, this method seems to gives the simplest one possible.

but you can make up any rule you want, like 83 80 84 83 88 95 83 102 112 83 122 135 83 148 164 83...

 

[dirk_mec1]

Yeah these tests reminded me of English class. Now students underline the gerund in the sentence below.

And I underlined the “ger” in one word and “und” in another. Wrong!

Could you please show me your line of reasoning regarding this sequence before we are going too far offtopic?

 

[jedishrfu]

I think we’ve covered everything so far and it’s time to close this thread.

Thanks to everyone for participating.

POST SCRIPT:

Most folks here believe its 83. I hinted at the answer by stopping my pros and cons list at 83 and left it for the OP to come up with pros and cons because ultimately its up to him how he thinks it should be answered. IQ tests are funny tests and it's never clear what the answer is at least to the uninititated.

Sometimes they will come up some really arcane reason that makes sense but its something you wouldn't even think to apply. It reminds me of the Bible Code, a book that was popular a few years ago where people find messages in the Bible by skipping every 10th word, letter or some similar scheme. Basically you can always invent a scheme to match the sequence you have and you can choose any book as the basis for the scheme.

https://en.wikipedia.org/wiki/Bible_code

Another more sophisticated example is the Beale's ciphers:

https://en.wikipedia.org/wiki/Beale_ciphers

which many believe are hoaxes to sell newspapers of the time.

And Veritaseum did a video on a similar sequence asking folks to predict the next number: