What's the next line in this number problem?

[JamesU]

What's the next line in this problem? (don't look it up and be cheap.)
1
11
21
1211
111221
312211
13112221
1113213211
31131211131221
13211311123113112211
11131221133112132113212221
3113112221232112111312211312113211
??

Please put the answer in white, and go as many lines as you can.

 

[JamesU]

NE1 going to try?

 

[Daih]

1
11
21
1211
111221
312211
13112221
1113213211
31131211131221
13211311123113112211
11131221133112132113212221
3113112221232112111312211312113211
1321132132111213122112311311222113111221131221111131221131211131231121113112221121321132132211331222113112221

The line underneath explains the line above.. e.g. 123 = one 1, one 2, one 3 = 111213... etc..

Arghh... gets tiring... I probably made a mistake somewhere in there too... oh well, you get the jist..

 

[JamesU]

It's not really hard, but what are all the extra 1's for in your first answer?

 

[Daih]

It's not really hard, but what are all the extra 1's for in your first answer?

I have NO idea

 

[JamesU]

 

[Drew888]

What's the next line in this problem? (don't look it up and be cheap.)
1
11
21
1211
111221
312211
13112221
1113213211
31131211131221
13211311123113112211
11131221133112132113212221
3113112221232112111312211312113211
??

Please put the answer in white, and go as many lines as you can.

Is it...
1321132132111213122112311311222113111221131221

 

[JamesU]

yes.

 

[PRodQuanta]

Kinda fun, that one is.
I had one of my friends on that for about a week one time, trying to solve it mathematically.

Paden Roder

 

[JamesU]

I took some science class during the summer. Our teacher didn't have much to say, so he gave us riddles, that was one of 'em

 

[Slaapkopf]

1
11
21
1211
111221
312211
13112221
1113213211
31131211131221
13211311123113112211
11131221133112132113212221
3113112221232112111312211312113211
1321132132111213122112311311222113111221131221
11131221131211131231121113112221121321132132211331222113112211
311311222113111231131112132112311321322112111312211312111322212311322113212221
132113213221133112132113311211131221121321131211132221123113112221131112311332111213211322211312113211
11131221131211132221232112111312212321123113112221121113122113111231133221121321132132211331121321231231121113122113322113111221131221[/color]

 

[mabs239]

Its a really good brain teser. But is there anything special about the series other than that?

 

[davee123]

Its a really good brain teser. But is there anything special about the series other than that?

Not really. Let's see...

There's only 1 number that starts off with a 2-- all the rest start with 1 or 3. All of them end in a 1.

Each digit in the series (left-aligning them) results in a 3-or-less length repeating sequence. So the 3rd digit (say) gets stuck in a loop starting at the 8th number in the series, repeating "1", "1", "2", such that the Nth number in the sequence's 3rd digit is predictable for N>=8. Each place follows a similar pattern with a loop length of 3 or 1. The 5th digit (for example) is always 1 starting at the 9th number in the sequence. And right-aligning the numbers results in 4-or-less length repeating sequences.

For each number in the sequence, if there are A 1's, B 2's and C 3's, then A >= B >= C. The percentage occurrences of 1's, 2's, and 3's seem to be convergent to roughly 49.5%, 32%, and 18.5% respectively (looking down to about the 50th number in the sequence).

There are probably some more things on that level of interesting, but nothing unexpected.

DaveE

 

[mabs239]

Dave
Thanks for the explanation. I couldn't see this page since long.

 

[John37]

Where does one start with this kinda stuff I'm a newbee