And what about this one:
1 1 1 2 1 1 2 1 1 1 1 1 2 2 1 What is the next line?I found several solutions, one better and couple of not really, but all of them don't match another property this sequence looks like to be following. Hmmm.
Oleg Tkachenko's Blog

Yet another google puzzleAnd what about this one: 1 1 1 2 1 1 2 1 1 1 1 1 2 2 1 What is the next line?I found several solutions, one better and couple of not really, but all of them don't match another property this sequence looks like to be following. Hmmm. Related Blog Posts
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The total of the first line is 1,
the total of the second line is 2,
the total of the third line is 3,
the total of the fourth line is 5,
the total of the fifth line is 8,
the total of the sixth line isn't 13?
1  Numer 1
1 1  Once a 1
2 1  Twice a 1
1 2 1 1  Once a 2 and once a 1
1 1 1 2 2 1  Once a 1, once a 2, twice a 1
It's only sayin what the previos line wrote. If you got 1 then you write "I got 1 of 1" 1 1. If you got "1111223" then you write "4 1 2 2 1 3" that could be read "four ones, two twos and one three".
Sorry bout my english :)
Bye!
1 1 1 1 1 1 1 2 1 2 1 1
and I am sure that I got it right :)
and is
1 1 1 1 2 2 1 1
and is
1 1 1 1 2 2 1 1
I agree with Dimitre on this, also when I first saw it I thought it more likely to be testing if you were the kind of geeky math guy who would know the sequence when they saw it rather than ability to find the next step of the sequence, although I suppose the two are related.
Dimitre, I know it's not software, but I'm a way lazy to create new categories... Didn't know anybody cares :)
bryan, I do believe there is something in that.
And I just don't believe googlers chose sequence starting from 1 and provided as much items as follow fibonacci numbers by accident.
They wanted to convolute the puzzle a bit more I think.
I think that it is not correct to use such problems in order to make conclusions about someone's intelligence based on whether this person offers the *single* solution we have in mind.
I remember having read somewhere that there are infinite number of solutions to the problem of finding the next element in a sequence, when only a finite number of the first elements of the sequence are known.
So, a person gives a valid solution (one of the infinite number of such solutions) that is different from the one solution we think exists. Then we say  look, this is not the solution... Sorry, you were not successful this time.
I find this absolutely unfair.
To summarize, such a test only evaluates whether a person's way of thinking is close to our own  not whether a person is really bright and intelligent.
Cheers,
Dimitre.
P.S. Oleg, the category for this stuff must be puzzles, not software.
Erich's right. The traditional sequence actually goes
3
1 3
1 1 1 3
3 1 1 3
1 3 2 1 1 3
...
If you're still stumped, a spoiler's at
http://mathworld.wolfram.com/ConwaySequence.html
(follow the first link on that page  I didn't paste that link here, because it gives away too much)
Answer is LZ algorithm :)
Next line is pairs (count, digit) for sequence of digits in previous line.
3 1 2 2 1 1
4 1 2 2
Answer is simple. Each next line contains pair of in previous line.
you know this is just proof that one metaphor fits all.
in a cosmological sense of course.
Okay, the sequence violates the fibonacci sum rule. But i guess this is a conincidence. So when posing the puzzle to other best to give one more line or so.
Sorry, i do not remember where i encountered this puzzle before, but this was the "correct" solution back then. Would be interesting if someone manages to come up with a plausible solution (i.e. induction rule) that maintains the sumtofibonacci property ;)
Yes, that's the best one I managed to come up with. But on the other hand, if you sum values in each row, you'll see another property, which this solution breaks.
Well, may be I'm wrong, first 1 is missing anyway to form a sequence of fibonacci numbers.
I don't think i'll take the fun out of it, if i give you the next few lines:
3 1 2 2 1 1
1 3 1 1 2 2 2 1
1 1 1 3 2 1 3 2 1 1
3 1 1 3 1 2 1 1 1 3 1 2 2 1
pretty fast growing, isn't it? ;)
Did you have the right solution amongst yours?