# Quick Number Puzzle
**URL:** https://boards.straightdope.com/t/quick-number-puzzle/364240
**Category:** In My Humble Opinion
**Created:** [July 12, 2006, 9:18pm UTC](https://boards.straightdope.com/t/quick-number-puzzle/364240 "2006-07-12T21:18:20Z")
**Posts on this page:** 20
**Page:** 2
### Author:  [@Antonius\_Block](https://boards.straightdope.com/u/Antonius_Block)
#### Post date: [July 13, 2006, 4:08am UTC](https://boards.straightdope.com/t/quick-number-puzzle/364240/21 "2006-07-13T04:08:24Z")
[MPSIMS]
I cheated (sort of) because that particular sequence of numbers has a significant meaning for me, so I only had to see the first two (19, 37) and the last (9?) to guess what the sequence was.
A few years ago, I was doing laboratory research on the formation of water clusters using mass spectrometry. Neutral water clusters are of the general formula (H[sub]2[/sub]0)[sub]n[/sub], but I also studied hydronium clusters (i.e. a hydrogen ion – _aka_ a proton – bound to water molecules) of formula H[sup]+/sup[sub]n[/sub]. The molecular weights of the latter clusters are 19, 37, 55, 73… (the difference of 18 in each case is due to the addition of one water molecule, H[sub]2[/sub]0 = 1+1+16). So, I had my mass spectrometer set to detect m/e ratios of that specific series of numbers, sometimes going on up to 505 (n=28) or more. There are some cluster sizes that are particularly stable, for which n is considered a “magic number” (an example is found at n=21).
[If anyone’s interested, [this PDF article](http://research.chem.psu.edu/awcgroup/PDFs/381.pdf) (PDF) gives an idea of this kind of research. The paper’s not from the lab in which I worked, but we did collaborate with those authors, Will Castleman’s group at Penn State.]
[/MPSIMS]
---
### Author:  [@Asimovian](https://boards.straightdope.com/u/Asimovian)
#### Post date: [July 13, 2006, 4:39am UTC](https://boards.straightdope.com/t/quick-number-puzzle/364240/22 "2006-07-13T04:39:20Z")
> [@Antonius Block](#):
>
> [MPSIMS]
> I cheated (sort of) because that particular sequence of numbers has a significant meaning for me, so I only had to see the first two (19, 37) and the last (9?) to guess what the sequence was.
>
> A few years ago, I was doing laboratory research on the formation of water clusters using mass spectrometry. Neutral water clusters are of the general formula (H[sub]2[/sub]0)[sub]n[/sub], but I also studied hydronium clusters (i.e. a hydrogen ion – _aka_ a proton – bound to water molecules) of formula H[sup]+/sup[sub]n[/sub]. The molecular weights of the latter clusters are 19, 37, 55, 73… (the difference of 18 in each case is due to the addition of one water molecule, H[sub]2[/sub]0 = 1+1+16). So, I had my mass spectrometer set to detect m/e ratios of that specific series of numbers, sometimes going on up to 505 (n=28) or more. There are some cluster sizes that are particularly stable, for which n is considered a “magic number” (an example is found at n=21).
>
> [If anyone’s interested, [this PDF article](http://research.chem.psu.edu/awcgroup/PDFs/381.pdf) (PDF) gives an idea of this kind of research. The paper’s not from the lab in which I worked, but we did collaborate with those authors, Will Castleman’s group at Penn State.]
> [/MPSIMS]
I’m going to take all of that to mean that those of us whose solution involved multiples of 18 + 1 were _more_ right than everyone else because we’re backed by SCIENCE! 😃
_I kid, I kid!!!_
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### Author:  [@GuanoLad](https://boards.straightdope.com/u/GuanoLad)
#### Post date: [July 13, 2006, 12:23pm UTC](https://boards.straightdope.com/t/quick-number-puzzle/364240/23 "2006-07-13T12:23:38Z")
> [@Tyrrell McAllister](#):
>
> I got the same answer as everyone else, but with different reasoning.
>
> I couldn’t help but notice that the first four terms are the values of
> n^5 - 15n^4 + 85n^3 - 225n^2 + 292n - 199
> for n = 1, 2, 3, 4. Evaluating at n=5 gives 91.
You should get out more.
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### Author:  [@photopat](https://boards.straightdope.com/u/photopat)
#### Post date: [July 13, 2006, 4:02pm UTC](https://boards.straightdope.com/t/quick-number-puzzle/364240/24 "2006-07-13T16:02:47Z")
> [@Robot Arm](#):
>
> I like the cut of your jib, **pat**.
Thanks **Rob** , but…how did you know I was circumsized? :dubious: (Looking over shoulder and…under desk)
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### Author:  [@The\_Chao\_Goes\_Mu](https://boards.straightdope.com/u/The_Chao_Goes_Mu)
#### Post date: [July 13, 2006, 4:52pm UTC](https://boards.straightdope.com/t/quick-number-puzzle/364240/25 "2006-07-13T16:52:37Z")
> [@Tyrrell McAllister](#):
>
> I got the same answer as everyone else, but with different reasoning.
>
> I couldn’t help but notice that the first four terms are the values of
> n^5 - 15n^4 + 85n^3 - 225n^2 + 292n - 199
> for n = 1, 2, 3, 4. Evaluating at n=5 gives 91.
Oh well pshhh, you did it the _easy_ way. 😃
I also got 91 but via the interval of 18 thing
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### Author:  [@gigi](https://boards.straightdope.com/u/gigi)
#### Post date: [July 13, 2006, 5:01pm UTC](https://boards.straightdope.com/t/quick-number-puzzle/364240/26 "2006-07-13T17:01:37Z")
91, via addition of 18. But this must have something to do with the sum of the digits being divisable by nine means a transposition??
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### Author:  [@gigi](https://boards.straightdope.com/u/gigi)
#### Post date: [July 13, 2006, 5:02pm UTC](https://boards.straightdope.com/t/quick-number-puzzle/364240/27 "2006-07-13T17:02:55Z")
Meaning (1) it’s a palindrome **and** (2) the increase is 18 works because of the sum of 9 thing???
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### Author:  [@photopat](https://boards.straightdope.com/u/photopat)
#### Post date: [July 13, 2006, 5:49pm UTC](https://boards.straightdope.com/t/quick-number-puzzle/364240/28 "2006-07-13T17:49:38Z")
FYI, I didn’t do any math, I just saw a pattern in the series. I assume others did as well?
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### Author:  [@Asimovian](https://boards.straightdope.com/u/Asimovian)
#### Post date: [July 13, 2006, 5:58pm UTC](https://boards.straightdope.com/t/quick-number-puzzle/364240/29 "2006-07-13T17:58:49Z")
> [@photopat](#):
>
> FYI, I didn’t do any math, I just saw a pattern in the series. I assume others did as well?
I’m not sure how literally you mean that. To me, noticing that each number in the series is 18 more than the previous number is a form of doing math, whether it’s conscious or not.
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### Author:  [@photopat](https://boards.straightdope.com/u/photopat)
#### Post date: [July 13, 2006, 6:44pm UTC](https://boards.straightdope.com/t/quick-number-puzzle/364240/30 "2006-07-13T18:44:15Z")
> [@Asimovian](#):
>
> I’m not sure how literally you mean that. To me, noticing that each number in the series is 18 more than the previous number is a form of doing math, whether it’s conscious or not.
I meant it quite literally. I saw that the middle number was 55 and the numbers on either side were mirror images. Therefore the last number should be the mirror of the first. It would have worked equally well with a series of letters.
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### Author:  [@Asimovian](https://boards.straightdope.com/u/Asimovian)
#### Post date: [July 13, 2006, 8:10pm UTC](https://boards.straightdope.com/t/quick-number-puzzle/364240/31 "2006-07-13T20:10:12Z")
> [@photopat](#):
>
> I meant it quite literally. I saw that the middle number was 55 and the numbers on either side were mirror images. Therefore the last number should be the mirror of the first. It would have worked equally well with a series of letters.
Ah…in that case, I definitely did use math, and didn’t notice the actual pattern until I read the puzzle’s answer. I know that at least a couple of other folks did it the same way I did.
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### Author:  [@Hal\_Briston](https://boards.straightdope.com/u/Hal_Briston)
#### Post date: [July 13, 2006, 9:32pm UTC](https://boards.straightdope.com/t/quick-number-puzzle/364240/32 "2006-07-13T21:32:19Z")
Sheesh…you’re all wrong wrong **wrong**!
19 - 37 - 55 - 73 - 9 = -155. It’s basic subtraction, people!
what?
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### Author:  [@rowrrbazzle](https://boards.straightdope.com/u/rowrrbazzle)
#### Post date: [July 13, 2006, 10:57pm UTC](https://boards.straightdope.com/t/quick-number-puzzle/364240/33 "2006-07-13T22:57:02Z")
I saw the palindrome in a few seconds. By Occam’s Razor, that’s the correct answer. 😉
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### Author:  [@Rhiannon8404](https://boards.straightdope.com/u/Rhiannon8404)
#### Post date: [July 13, 2006, 11:08pm UTC](https://boards.straightdope.com/t/quick-number-puzzle/364240/34 "2006-07-13T23:08:44Z")
> [@Robot Arm](#):
>
> The first thing I thought of was…a palindrome. The same sequence backwards and forwards, the last number has to be 1.
This was my answer as well.
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### Author:  [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)
#### Post date: [July 14, 2006, 3:12am UTC](https://boards.straightdope.com/t/quick-number-puzzle/364240/35 "2006-07-14T03:12:24Z")
There’s a difference between the palindrome solution and the mathematical solution.
Consider: 19 - 37 - 55 - 73 - 91 - What’s the next number in this sequence?
The palindrome spotters are going to say there is no next number; the sequence is complete. The mathematicans would say it’s an open-ended sequence and the next number is clearly 109.
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### Author:  [@Sage\_Rat](https://boards.straightdope.com/u/Sage_Rat)
#### Post date: [July 14, 2006, 10:22am UTC](https://boards.straightdope.com/t/quick-number-puzzle/364240/36 "2006-07-14T10:22:42Z")
I spotted it as a palindrome.
And given that that was the author’s intention, the fact that there is a second possible solution is simply an anomaly based on the random sequence they chose.
Fibonacci:
1, 1, 2, 3, 5, 8 -\> 18 15 23 32 51 81
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### Author:  [@Harmonious\_Discord](https://boards.straightdope.com/u/Harmonious_Discord)
#### Post date: [July 14, 2006, 1:02pm UTC](https://boards.straightdope.com/t/quick-number-puzzle/364240/37 "2006-07-14T13:02:44Z")
I found the answer that the puzzle makers had wanted, quickly by patern recognition.
The answer was immediately recognized as the correct solution by memory of this puzzle’s use so many times over the years.
19 to 37 is a difference of 8 so consider that for Stainz method, and it doesn’t figure. His method was not correct. It worked because he missed the difference of 19 to 37 and resulted in a erronious answer that proved correct.
I haven’t seen results by anyone charting and projection of the line to find a solution. It could led to the correct answer if the chart was analysed as a trend.
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### Author:  [@Malacandra](https://boards.straightdope.com/u/Malacandra)
#### Post date: [July 14, 2006, 1:39pm UTC](https://boards.straightdope.com/t/quick-number-puzzle/364240/38 "2006-07-14T13:39:49Z")
> [@Harmonious Discord](#):
>
> 19 to 37 is a difference of 8 so consider that for Stainz method, and it doesn’t figure. His method was not correct. It worked because he missed the difference of 19 to 37 and resulted in a erronious answer that proved correct.
What numbering system are you using? :dubious:
> [@Harmonious Discord](#):
>
> I haven’t seen results by anyone charting and projection of the line to find a solution. It could led to the correct answer if the chart was analysed as a trend.
The same thing. You’ve got a straight line graph there of the classic form y = mx + c, where m=18 and c=1. But equations give more accurate results than graphs, 'cos they don’t depend on your ability with ruler, line and squared paper.
@ **Tyrrell McAllister** : Bwuh? :eek:
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### Author:  [@Leaffan](https://boards.straightdope.com/u/Leaffan)
#### Post date: [July 14, 2006, 2:19pm UTC](https://boards.straightdope.com/t/quick-number-puzzle/364240/39 "2006-07-14T14:19:51Z")
First I noticed they added to 10; then I noticed the series.
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### Author:  [@Harmonious\_Discord](https://boards.straightdope.com/u/Harmonious_Discord)
#### Post date: [July 14, 2006, 2:48pm UTC](https://boards.straightdope.com/t/quick-number-puzzle/364240/40 "2006-07-14T14:48:41Z")
> [@Malacandra](#):
>
> What numbering system are you using? :dubious:
Dah! :dubious: It’s the hyper-reality quantum accelerated math. I learned it from the new release of “Hyper-reality Quantum Accelerated Math for Dummies” book. Can’t you tell? :mad: Hee hee hee. 😕
> [@Malacandra](#):
>
> The same thing. You’ve got a straight line graph there of the classic form y = mx + c, where m=18 and c=1. But equations give more accurate results than graphs, 'cos they don’t depend on your ability with ruler, line and squared paper.
>
> @ **Tyrrell McAllister** : Bwuh? :eek:
I realize that. Stainz want methods and ploting a chart is a different method, and not a formula calculation. This was a quest for the method one might use. 🆒
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