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

    1. 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.

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

  2. 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).

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

  4. 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.

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

  6. 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…

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

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

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