Please do NOT post your answer, but do say if you think you have solved the puzzle and how long it took. Solution on Monday.

What row of numbers comes next?
1
11
21
1211
111221
312211
13112221
I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.

1. Conor Magee says:

Done.

2. Eddie says:

I reckon I’m smart enough to get this.

3. Goliath says:

School puzzle – I never forgot how to solve it.

4. I haven’t the foggiest

5. Drew says:

This was a puzzle in Star Wars Knights of the Old Republic.

6. beanfeast says:

I was looking at it for about 45 seconds with no clue and suddenly out of nowhere I realised what was going on.

1. Stevie says:

Similar thing happened to me.

2. chakolate says:

Then you are an excellent pattern-recognizer. It only took me about a millisecond, but that’s because I’ve seen it before. The first time I didn’t get it at all.

3. Merari says:

Same kind of thing. I don’t know whether I got it right, but I think my answer is pretty interesting anyway.

7. mittfh says:

I’m sure I’ve seen this one before – a puzzle from a few years ago, perhaps? I have a feeling it was one of those that’s so obvious and logical when you know the rules (which can be used to expand the series ad infinitum), but of course deciphering the rules is easier said than done (and I’ve forgotten them).

1. Martha says:

I agree – it took about 10 seconds to remember what the rule was

8. -viki says:

🙂 took less than “1310” seconds to suss this one!

1. One Eyed Jack says:

+1

Good puzzle. As is often the case with RW’s puzzles it makes a point about one’s assumptions. Took me about 5 minutes.

10. ChrisR says:

seen before – got immediately – can’t remember how long it took me the first time though

11. Alix says:

I know this one and love it! Originally, it took us 10 minutes and lots of fun.

12. Steve says:

I’m currently puzzled !

13. NickC says:

I am the “1114” Comment

1. Turd says:

Actually you are the 1113, do not count replies as the number will change when people reply.

14. issahamati says:

it took me 10 minutes to solve it

15. Tom says:

Had several tries on this one, none of which turned out to be the correct answer. Suddenly got it after 10 minutes or so.

Once you get it, it is obviously the correct answer.

16. Turd says:

I got it while reading the number half way

17. ChrisR says:

11 was a racehorse
22 was 12
1111 race
22112

1. chakolate says:

Heh – nice!

18. Chris says:

A few seconds to guess, a few 10s of seconds to check. A few minutes wring Python code to test many iterations, and no digit higher than 3 ever appears – now I’m thinking I should prove it.

1. Chris says:

OK that was quite simple too, given a few seconds thought – you couldn’t get 1111 because the previous line that could produce that would actually produce 21. etc.

2. ChrisR says:

so, is it a ‘diverging’ and non-repeating sequence, or does it tend to a limit? and is that true for whatever we start with? I remember the ‘Life’ program on the old BBCB / Atari computers – lots of fun seeing what difference a small change at the start made

3. 1A2N1O says:

Chris R
My gut feel is that it is repeating and tends to a limit – but gut feels aren’t very scientific are they?

4. ChrisR says:

5. 1A2N1O says:

Chris R
My gut feel is that it is repeating and tends to a limit – but gut feels aren’t very scientific are they?

19. Albrecht says:

I know a guy who programmed a voice-recognition system for an electric company so that people could send the requiered information by phone. He hated when people did this…

20. Edgar says:

21. Gene says:

I’ve been waiting for this one to come along.

1. Eddie says:

Well? Now it’s here how do you feel?

22. edwardv says:

After reading the first three or four lines of numbers I recalled the puzzle. A good one.

23. James says:

I actually prefer an alternate version…
1
11
21
1211
1231
131221
132231

1. chakolate says:

It’s more compact, but you lose information. It’s impossible to reconstruct the previous line.

24. I got the answer as soon as i got to the second line, but probably only because I remember seeing the puzzle several years ago. Originally it probably took me about 30 or 40 seconds.

25. Miss Chili says:

Gah! I’ve never seen this puzzle before, nor can I work it out.

1. Chakolate says:

I first saw it in a lecture by John Conway, and he referred to it as the silliest possible sequence. Does that help?

26. Matt says:

My question is, would there ever be a number above 3? How would you prove that?

1. No there wouldn’t.

2. Eddie says:

Nice proof!