The next row is "fuck you, clown."
58008918.
Oh, wait, that's the 12 year old's answer
I couldn't figure it out, so I Googled the last number in the original post. The top three hits, and at least five of the top 10, are explanations of just this problem. So I guess the line after the one ajay gave would be 1113213211, right?
All we need to outwit five-year-olds once and for all are neural computer interfaces and wi-fi in our heads.
I couldn't get it either. I also don't think five-year-olds would get it. Mine would stare for a bit and then talk about karate or demand to know if Santa is real.
I would have never gotten it, and neither would my six year old. The (almost) 9 year old is good at this sort of thing, though.
I still like my answer better.
The first number makes no sense.
We talked about this brainteaser once before -- you need a seed to start it with. '1' is as good as anything.
01 would make sense but would make it too easy.
11: if the rules change that breaks the pattern. If the pattern breaks once, why should it continue?
Twenty-odd years ago, as a freshman or sophomore still planning a major in mathematics, I went to a lecture at which John Con/way presented this very problem in much the same way, although I think the specifics were something like "if you get this, you probably don't think like a mathematician" or something like that. (I got it right away, and, sure enough, shortly thereafter hit a serious wall and flamed out of math quite dramatically.)
"if you get this, you probably don't think like a mathematician"
What a lot of mathematicians we are!
And wouldn't it be super cool if John Conway showed up? Why are we google-proofing his name?
15: Can't you say the same thing about the Fibonacci sequence? You need two initial elements before the rule can start working. I don't think it destroys the rule to require a starting point.
19: On reflection, no reason, other than that I find Unfogged google-proofing practices strange and confusing.
There doesn't seem to be any pattern either vertically or horizontally or diagonally.
Sometimes I don't think you all even listen to the song the requisite three times.
What's the next row?
Unser Paradox war dies: Heebie kann nicht immer richtig sein, da jede Handlungsweise mit Heebies Aussagen in Übereinstimmung zu bringen sei.
"if you get this, you probably don't think like a mathematician"
I find this weird. Was he trying to make some sort of Wo/fram-esque "a new k/nd of sc/ence" distinction?
Naturally, I recognized the sequence in question straight off.
The rule is:
S(n), where n < 0, is empty.
S(0) = 1
S(n), where n mod 3 = 0: rotate the first two digits of S(n-1) and append S(n-2)
S(n), where n mod 3 == 1: rotate the first two digits of S(n-1) and drop (what is now) the second, and the prepend to the result the first two digits of S(n-2), reverse all that, and prepend 1.
S(n), where n mod 3 == 2: rotate all the digits of S(n-1) one spot to the left, then add (n+1)/3 to the first digit.
This, as will plainly be seen, generates the following:
S(0): 1
S(1): 11
S(2): 21
S(3): 1211
S(4): 111221
S(5): 312211
S(6): 132211111221
Of course, most of us would have arrived at neb's solution long before the age of 5.
20: totally not the same.
In my head, I know why.
People study Fibonacci sequences that are seeded with different initial values. We could say that the sequence in the OP represents a class of sequences, and tomorrow I'll post the next case, ie a_o=1.1 .
The fibonacci sequence uses a single data type. This sequence uses two data types, indexed by sequence rank mod 2, except for the first sequence, which uses a totally different coding scheme. Intolerable.
||
Fun. Noisy at the beginning, but do use sound.
|>
25: It was a long time ago, and I'm surely not quoting him verbatim, but I doubt it was meant seriously. I think he was just trying to be funny and offer a clue along the lines of "think outside the box." (He did go on to demonstrate some putatively interesting properties of the sequence, and googling around it looks like he published on it right around the time I have in mind.)
Ironically, I used "sequence" to mean two different things in 31. I'm sure it was clear to the kindergartners.
Huh. It has its own wikipedia article.
In my head, I know why.
This is my primary defense of all arguments and assertions. And it's true! Why can't you just accept that?
Mulato Astatke, Ethiopian Jazz: http://www.youtube.com/watch?v=6vq3n4plTM0
It has to be a puzzle for a five-year-old because the third line is ungrammatical. Five-year-olds don't care, but the rest of us are used to nouns declining.
I stayed up last night watching math videos on youtube:
http://www.youtube.com/user/DrJamesTanton
My dad actually gave this as a puzzle to me when I was about eight. I didn't get it, despite hours of agonizing over it. Maybe that was because I was past my prime.
I didn't see it when I was 5, but I know that I was a pedantic little shit at that age and I would have said that 1 means "one", not "ones" or "x one", and therefore the proposed answer was wrong. I'm still a pedantic little shit, and I still say that.
Kindergarteners sing The Ramones' "Judy Is A Punk"
44 kind of puts a tiny dent in my cranky, evil-hearted indifference to kids. I almost phrased that in a way that would have been really, really problematic given the demographics of the participants.
46: I was assuming that this was at the school of the same name here in Mpls., but the demographics tend to argue against that, as the Su//ivan School here seems to have a pretty significant population of Somali students. I dunno.
Hey! Listen to the great song, you guys!
It's not a thumping song, that's true.
Well, that's why I'm not listening to it.
I'm not listening to it because I don't want to reach to turn on the speakers.
I'm not listening to it because my fondness for heebie remains undimmed despite the fact that I haven't particularly liked any song she's ever posted, and why mess with that?
Well, I'm a sucker for someone being fond of me, so you're forgiven.
The song was okay, but I'm not really into country.
I'm confused about what in particular was noteworthy about that song. Not ironically. It wasn't awful or anything. Admittedly, I have only a pre-intellectual, instinctive lumpen-proletarian understanding of Country & Western Music.
Are there any alternate histories where jug bands and skiffle take the top spots as the new, post-Western Classical Tradition, world musics? 'Cause that would be awesome. Will Shade is the Louis Armstrong and John Lennon just keeps going with the Quarrymen to international stardom. It could be "gaspunk", an alternate 1990s where WWII and the Bomb had never happened and the US political landscape still included Populists and Free Silver advocates in positions of influence. Limited TV wouldn't have replaced movies, and New Deal co-op towns like Greenbelt would exist in place of post-war suburbia all over the country.
I've also been thinking it would be fun to write a "horsepunk" novel about Karl Marx in an alternate 1830s where Napoleon never lost a war and created a Europe-wide empire with all kinds of subject nationalities producing assassins right and left, and Vidocq is an anarchist agitator. And he could be friends with Bakunin, so the First International would never split...anyway, there'd definitely be something about the anarchist watchmaking guilds in Switzerland.
Oooh: In the gaspunk one, JFK could be the retired corrupt head of the Boston Democratic machine.
Sleepy Palestine where the British Mandate lasted into the early 1960s, and by that time everyone was pretty much getting along.
Set part of it in a social-democratic United South America, a loose federation of the Spanish-speaking South American countries. And a functional Spanish Republic with areas that exist as semi-autonomous anarchist-oriented "Voluntary Zones". Bunuel would be the Spielberg of the Spanish-speaking world. Gaudi and Dali would be bigger architectural influences than Wright and Johnson.
Populists I get, but free silver? If we had a New Deal, we almost certainly went off the gold standard.
58.3 could be merged with my AH concept of liberation theology becoming the mainstream of Catholicism.
One of the main characters in the horsepunk one could be a young clerk of aristocratic lineage but very modest means who first gets embroiled in a nationalist-aristocratic plot to liberate Italy from French rule. and then falls in with the anarchists and is eventually converted to their beliefs.
And there could be a young middle-class woman who gets caught up in the plotting and starts to critique patriarchy and starts working with an underground proto-feminist organization created by Mary Shelley.
Maybe there'd be a printer's strike in Toulouse or something that would start spreading from city to city all over the empire. And then it would be time to write the second book.
So who's the dashing anarchist Mary Sue protagonist?
59: Yeah, that's a point I guess. Maybe say that Free Silver had had a much larger influence than it actually did, making things ripe for bigger shifts in national politics. And have no Palmer Raids, and perhaps a more-successful Bonus Army occupation?
63: Huh. I was thinking of that character as the priggish dork who has to get beaten up a few times before he can see the contradictions in his ideology. If it's a Mary Sue you seek, the young Marx is probably the best bet.
I was perhaps leaning too much on the idea that he'd be dashing.
Oh, one thing I forgot to mention is that the horsepunk* one is inspired by a rather drier book called Karl Marx and the Anarchists which totally ought to be this kind of Boys' Own Paper adventure, except leftier.
*Part of the "horse" part is that, prior to having really efficient steam engines, Napoleon gets Europe oriented towards animal-traction powered machinery.
re: 67.1
I was struck by how 'Boy's Own' the life of the young Stalin was, in Young Stalin. Daring bank-robberies, escapes disguised as a women, horse-rides across Caucasian mountain tops carrying illegal printing equipment, escape from exile (again and again and again), etc.
that I haven't particularly liked any song she's ever posted, and why mess with that?
I just listened to this song, I agree with 56 that it seems kind of generic country.
My favorite of the songs that H-G has linked is still Jose Cuervo, which I genuinely liked.
20: Actually, you can run the Fibonacci sequence in both directions: ... -8, 5, -3, 2, -1, 1, 0, 1, 1, 2, 3, 5, 8, ...
That still leaves an arbitrary choice of two elements, though, it's just that they don't have to be the first two. But the way sequences are usually taught, you have an arbitrary choice of initial elements, and then some rule that kicks in at some point, and we only consider sequences running in the positive direction.
Are there any alternate histories where jug bands and skiffle take the top spots as the new, post-Western Classical Tradition, world musics?
That would be the history where Mel Lyman attains his goal of world domination. Maria Muldauer would be Mother of the People, and Jim Kweskin would head the secret police.
Gaudi and Dali would be bigger architectural influences than Wright and Johnson.
Aw, yeah. I used to dream about what Manhattan would look like in a world where Gaudi had received the praise and attention that bloody Le Corbusier and the Bauhaus mob got. Like a termite mound five miles high.
I dream of a world in which pop singers show their seriousness and authenticity not by covering songs like "Goodnight Irene" and "Single Girl, Married Girl", but by doing songs like I'm Gonna Wash My Hands of You.
Too cheerful. I dream of a world in which pop singers show their authenticity by singing this.
Here's a nice little nerdy brain teaser I only learned about this morning:
How I need a drink, alcoholic in nature, after the heavy lectures involving quantum mechanics!
Which well known constant does this sentence represent?
The only thing that makes that possible is that there are so few constants that you could reasonably expect a general audience to guess. The first one I tried worked.
I've got a couple of non-mathematical sequence puzzles involving trivia here and here. Both puzzles are original by yours truly. There is a definite ordering to the names in each list.
First one's Wisconsin -- I knew enough to spot the principle, but my geography's weak enough that I needed Google to tell me which answer fit.
79: Wikipedia might help a bit there, but you have to find the right bird to search on. One of the other sites that came up when I Google'd that bird would be even more helpful...
80, continued: And there's another way to Google that question where the results are basically a dead giveaway.
The hint on that question was "This may require an encyclopedia," because the relevant bit of trivia is not one most people have memorized. It's just a pattern that appealed to a twisted mind like mine when I first encountered it (oddly, in an educational graphic given away with a kid's meal from KFC several years ago...).