[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 (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’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.
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.
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.
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.
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.
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.
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.
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.
