Nuber 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 gonna try????

Daih

1
11
21
1211
111221
312211
13112221
1113213211
31131211131221
13211311123113112211
11131221133112132113212221
3113112221232112111312211312113211
13211321321112131221123113112221131112211312211111312211312111312311211 13112221121321132132211331222113112221

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

I have NO idea

JamesU

Drew888

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
31131122211311123113111213211231132132211211131221131211132221231132211 3212221
13211321322113311213211331121113122112132113121113222112311311222113111 2311332111213211322211312113211
11131221131211132221232112111312212321123113112221121113122113111231133 221121321132132211331121321231231121113122113322113111221131221

mabs239

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

davee123

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 explaination. I couldn't see this page since long.

John37

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