What is the next line in this math puzzle?

Question

1
1 1
2 1
1 2 1 1
1 2 3 1
2 1 1 2 1 3
?

Answer 1

six possible answers

1 3 2 2 3 1
3 1 2 2 1 3
2 2 3 1 1 3
2 2 1 3 3 1
1 3 3 1 2 2
3 1 1 3 2 2

every line describes the previous line by counting the frequency of each digit

e.g. the line "1 2 1 1" consists of
"one 2, three 1" and therefore gives the next line
" 1 2 3 1"

Challenge 1: prove that every subsequent line consists of 6 digits
Challenge 2: the sequence will eventually end up in a cyclic pattern. Which?

Answer 2

1 1 3 2 1 3

Answer 3

its actually suppose to be

1
11
21
1211
111221
312211
13112221
1113213211


you forgot in the 4th line

only 1 1 1 2 2 1

you forgot to include the 1 (one)

but... i answered this before...


with additional info because i gave the answer to the 9th line

1211 you look the first group of 1's and say '11'; then you see the next group of 2's and say "12"; finally you see the last group of 1's and say "'21', giving the whole next member of the sequence 111221.

But what if instead of taking partial views of the digits of 1211 you take exhaustive views of all the digits, as encountered, and say the total of each? In doing so, the next member to 1211 would be 3112 instead of 111221

so the answer would be 31131211131221

http://answers.yahoo.com/question/index;_ylt=AgQzVnXR.UfGDy6jPjs6fRnsy6IX?qid=20060712051057AAS19l9

check ya later ♥

Answer 4

312213 Should be the correct answer

Answer 5

312213