please hope me

October 29, 2006 6:10 PM

What is the next number in this sequence: 4, 58, 40, 27, 18, 12, 8, ? Please give your explanation.

Came up on this question in an aptitude test and it stumped me.

posted by scodger to grab bag (41 comments total)

The Online Encyclopedia of Integer Sequences is stumped as well.
posted by euphorb at 6:24 PM on October 29, 2006

Are you sure that:

1) You didnt make a transcription error or
2) Some important context is missing (aptitude for what?)

The Encyclopedia Of Integer Sequences even includes stuff like subway station numbers. Its fairly complete and would welcome this as a new entry.
posted by vacapinta at 6:29 PM on October 29, 2006

Maybe I'm nuts, but

Ignore the first 4 for a second

The difference between the number and the next number is

18
13
9
6
4

9 is half of 18, 6.5 is half of 13 (6 if you round down), 4.5 is half of 9 (4 if you round down), so perhaps the next number is "5"? (8-3)
posted by JakeWalker at 6:29 PM on October 29, 2006

5 or 6.. Thats just from plotting them out and following the trend of the graph.
posted by phyle at 6:29 PM on October 29, 2006

Well, yes, if you ignore the first 4 then the answer is 4 or 5.

Thats assuming an aptitude test has a complex binomial sequence it expects you tu understand.
posted by vacapinta at 6:33 PM on October 29, 2006

The first number seems to be an anomaly. For the rest, the next number should be 5. Here's why:

58     -18
40     -13
27       -9
18       -6
12       -4
8

Taking the second sequence:

-18     +5
-13     +4
-9       +3
-6       +2
-4

It's obvious that the next value in the second derivative is +1, which means the next value in the first derivative is -3, which means the next value in the primary sequence is 5.

Extrapolating the first part, the next value in the second derivative should be +6, meaning that the next value in the first derivative should have been -24, so the first value in the primary series should have been 82, not 4. 4 makes no sense and can't be reconciled with the rest of the values we're seeing.
posted by Steven C. Den Beste at 6:37 PM on October 29, 2006

Well, you have also stumped the Online Encyclopedia of Number Sequences, normally a good tool for these things.
Which leads me to think there's an error in the sequence. Without the leading 4, if you just had 58, 40,27,18,12,8, the differences between the numbers are 18,13,9,6,4. The differences between those numbers are 5,4,3,2. So the next one there is 1, which makes the next number in the prior sequence 3 (18,13,9,6,4,3), which makes the next number is the subject sequence 5. (58,40,27,18,12,8,5)
But that doesn't explain the 4.
posted by beagle at 6:42 PM on October 29, 2006

For these kinds of tests, if we had a question-

1, 2, 3, 4, 1.. we would expect the next answer to be 2. These things can loop. So I think 4 or 5 is correct, the 4 is not really an anomaly, its just a looping sequence?
posted by phyle at 6:44 PM on October 29, 2006

1. It was an officer recruitment test for the NZ army
2. I am 100% sure what I was given is what is here

This is the only question I couldn't answer, but they took in the sheets of paper I used for working and sent them to the psychologists for testing, so maybe it is meant to be unanswerable.
posted by scodger at 6:44 PM on October 29, 2006

It's possible that the anomalous first value was put in deliberately to see if you'd be stumped by it, or would correctly conclude that it didn't belong there.
posted by Steven C. Den Beste at 6:52 PM on October 29, 2006

Here's my explaination for the pattern, as well as the leading value...
5
+3
8
+4
12
+6
18
+9
27
+13
40
+18
58
+24
oh hell I forgot to type the 82... so... HEY .. 4 is like 82
posted by shownomercy at 6:53 PM on October 29, 2006

If the first digit is supposed to be a 4, I'd go with 116, on the basis that you're looking not at a relationship between each number, but that it's an arbitrary six-number pattern that is doubled when it is repeated. I prefer it to the answer of 5 that has been given here, because it accounts for all the numbers given. My guess is that it's a lateral thinking problem, and the relationship between the other numbers is a red herring.
posted by graymouser at 6:56 PM on October 29, 2006

I don't know, but what is the next in this sequence:
14,23,28,33,42,51,59,68,77,86
posted by caddis at 7:10 PM on October 29, 2006

If you ignore the 4 completely then the sequence is trivially easy: each number is 2/3 of the previous one, so the next number is 5. But by that logic the first number should be 87.
posted by Hogshead at 7:12 PM on October 29, 2006

With thanks to JakeWalker for the clue of looking at the differences, let's examine them as a series.

If we put aside for the moment the first number (n1), our series of differences looks like this:

n2-n3 = 18
n3-n4= 13 (18-5)
n4-n5= 9 (13-4)
n5-n6= 6 (9-3)
n6-n7= 4 (6-2)

Each difference, then, can be expressed as a function of the previous difference minus one of a descending series of integers. The next integer in the series is 1, which subtracted from the previous difference yields 3.

The next number in the sequence (n8) will be the difference between n7 and 3, i.e., 8-3=5.

The first difference in the sequence (n1-n2) should should be 24 (i.e., 18+6) and so the first number in the sequence (n1) should be 58+24 = 82.

If I'm right, then n9 is 2 (i.e., 5-(3+0)), and n10 is 0 (i.e., 2-(3+(-1))).

I tried for a while to express each number in the sequence as a function of the previous number, but then my brain began to hurt. Anyone? (This probably will be much simpler to express in reverse order, beginning with 0.)
posted by La Cieca at 7:13 PM on October 29, 2006

You didnt follow my subway link above, did you caddis?
posted by vacapinta at 7:16 PM on October 29, 2006

no, I did not
posted by caddis at 7:19 PM on October 29, 2006

Could it be something like a Poisson distribution or some kind of decay curve? If you plot it out, there's a rapid onset phase (from 4 to 58) then it just decays in a nice smooth curve.

(It actually looks like the kind of data you get from pharmacokinetic experiments measuring drug concentration in the blood, which is a function of uptake and excretion.)
posted by Quietgal at 7:20 PM on October 29, 2006

How many pages was the test? How many questions were on it? Is it possible that this question was referencing other problems on the test that were in some way related?
posted by 23skidoo at 7:22 PM on October 29, 2006

my head just mathsploded.

I do like the suggestion that the question was made to be unanswerable; I would think that a question like that, combined with a "show your work" requirement, would bring about some interesting results.

...and because stuff like this is really, really hard to me.
posted by craven_morhead at 7:26 PM on October 29, 2006

I agree with Steven C. Den Beste. The 4 is a red herring (it is a number known to have special significance to al Qaeda and the Taliban, after all, and was clearly inserted by them as a diversionary tactic); 5 is the next number. Ignore the jihadist tricks! Bomb target number 5!
posted by Dasein at 7:44 PM on October 29, 2006

It's your Kobayashi Maru!

Or could the sequence be representational and not mathematical?
posted by Joleta at 8:07 PM on October 29, 2006

I think 116 is the best answer so far. I ran this by my staff mathmatician and he couldn't come up with anything; he liked the guess of 5 that others have floated.

If it's nonrepresentational, it's not obvious.
- It's not the number of letters in each word in some phrase; no words with 58 letters. Could be number of words in sentences (or number of sentences in first few paragraphs) of some famous text, but that's a stretch to expect you to know by rote.
- It doesn't match any of the obvious categories (days of week, weeks per year, second per day, etc; continents; planets on solar system...)
- If we spell out the words we get:
four
fifty-eight
forty
twenty-seven
eighteen
twelve
eight
This doesn't make anything obvious. There are a lot of repeated phonemes (fo-fi-fo twe-ei-twe-ei), but I'm not sure where to go with that.
- They don't translate to an interesting pattern of hands on a clock... assuming 4:58, 4:02, 7:18, 12:08.
- There are a lot of numbers repeated, but again, I'm not seeing anything obvious to do with this. There are:
two 4s
two 8s
two 2s
two 1s
one 5
one 0
one 7
no 3, 6, or 9.
posted by LobsterMitten at 8:41 PM on October 29, 2006

I tried to put this visually; it is the same solution as other have suggested:



5 would be the last number. But if this solution were correct the first number would be 82, not 4. Hmmm.
posted by catburger at 8:51 PM on October 29, 2006

D'oh, the image didn't show up. Here it is
posted by catburger at 8:51 PM on October 29, 2006

Looking at the periodic table, we find that:

4 = Be
58 = Ce
40 = Zr
27 = Co
18 = Ar
12 = Mg
8 = O

So it's obviously whatever element finishes this: "BeCeZrCoArMgO__".
posted by Guy Smiley at 9:01 PM on October 29, 2006 [1 favorite has favorites]

For what its worth the cubic function people here are using is:

(678 - 209*n + 24*n^2 - n^3)/6

For n=1, then answer is 82. For n=8, the answer is 5.
posted by vacapinta at 9:07 PM on October 29, 2006

Can someone explain 'hope me'? I checked the FAQ and didn't see it. It seems to be a metafilter-specific meme...
posted by PercussivePaul at 9:14 PM on October 29, 2006

PercussivePaul: check out the InJoke wiki entry.
posted by niles at 9:17 PM on October 29, 2006

ooh. that page should be linked in the FAQ!
thanks.
posted by PercussivePaul at 9:40 PM on October 29, 2006

whoops. I think we all missed the point here. The answer is easy, the answer is 4; anyone can see that there is a simple pattern ignoring the first number. Many above have arrived at this conclusion that 4 is the correct answer.

However, the question askers are certainly not interested in simple maff skillz. If we are really reading a question from a NZ officer test, I made the assumption that the army is more interested in one's ability to to filter information as well as recognize patterns; they want someone confident in their answers, who will make decisive actions despite slightly conflicting evidence. This question is a test to determine if the smart people they are testing are meant for academia/intelligence ("there are a variety of answers to consider, blahblahblah") or command. ("THE ANSWER IS 4 THERE WAS AN ERROR OF COURSE ITS 4 LETS GO BOYS") This question divides Abstract thinkers who sit at a desk planning, or Practical thinkers who determine which soldier has to die as the insurgents close in.

I like sports, So my guess is 4. let's go, motherfuckers!
posted by wuzandfuzz at 10:06 PM on October 29, 2006

I know a lot of Kiwi Army officers - few of them could have answered this question given the reasoning laid out here (and I have no idea what the answer is either).
posted by dangerousdan at 11:15 PM on October 29, 2006

ooops i meant 5, heh. guess that means i'd be a private. thats what you get when you barely read the thread. Im referring to den beste's answer.
posted by wuzandfuzz at 11:55 PM on October 29, 2006

Caddis: 96.
posted by emelenjr at 3:14 AM on October 30, 2006

Looks like an interesting context test: The first number is not an anomoly; this is a military exam and the situation they're referring to is somewhere between an artillery shot (lots of positive energy at the beginning that drains away over time) and a rocket launch (huge amounts of weight at the beginning, but as you burn off fuel it takes less and less to keep you in the air).

I suspect the point is going through the thought process of "what systems do I know about that would have traits like this".
posted by effugas at 3:58 AM on October 30, 2006

effugas: except that it's an entrance exam and the person taking the test would not have the knowledge (yet) of said systems to mentally go through.
posted by smcniven at 4:27 AM on October 30, 2006

Is possible that this is item #4 on the test?

Also, did the original test ask the applicant to "show your work" or "give an explanation," or was the task simply to cough up a number? If the point of the exercise was to see what process you would follow when given inaccurate data, I can see some kind of point to this as an aptitude test. Otherwise, it's pretty standard SAT-style math with a typo.
posted by La Cieca at 5:27 AM on October 30, 2006

I would imagine the point of the question was to see how much time you would waste trying to solve an unsolveable problem. Since you said it was the only question you left unanswered you are probably okay.
posted by Bonzai at 7:45 AM on October 30, 2006

It is 4, the first four is there to indicate that when the loop closes you start over again.
posted by I Foody at 9:34 AM on October 30, 2006

58-40=18
40-27=13 (difference 18-13=5)
27-18=9 (diference 13-9=4)
18-12=6 (difference 9-6=3)
12-8=4 (difference 6-4=2)
4-3=1
Is this right?
posted by madstop1 at 9:22 PM on October 30, 2006

Madstop:
No. To be consistent, instead of "4-3=1", your last line would have to be:
8-5=3 (difference 4-3=1), indicating that 5 is the next number.
That result is arrived at, above, by various respondants. However, as most of them have pointed out, that doesn't account for the 4 which starts off the sequence. And working backward, this pattern would mean that the number before 58 should be 82, not 4.
posted by beagle at 5:46 AM on October 31, 2006