coverOn Friday I set this puzzle…..

What row of numbers comes next?1
If you have not tried to solve it, have a go now.  For everyone else the answer is after the break.
The next row is

From the second line onwards, every line describes the line before it in words…..

One One
Two Ones
One Two One One

Did you solve it?
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 didn’t get it until this morning when I was about to leave for work – a bit of a eureka moment. 🙂
    Very easy to understand or explain, too. A nice little trick!

  2. Good one. Although the explanation of the answer doesn’t seem quite right: no line describes the line before *in words* because all of the lines are in numbers, not words.

    1. Well, I thought too at first that it was in a different system, but came up with nothing. I had a feeling I was overthinking it, but simply couldn’t find the answer.

  3. Crazy coincidence – this morning I just saw this exact puzzle in a book I am reading – The Cuckoo’s Egg by Cliff Stoll – pg 313.

    1. Andy,
      I just finished re-reading “The Cuckoo’s Egg” a couple weeks ago – great book!

      As for the puzzle, I came across it a couple years ago & wasn’t able to figure it out.

  4. In order for the number ‘4’ to appear in the sequence, there needs to be four in a row of a particular number, ‘N’, and the string in the relevant line would have to contain “4 Ns” in a row. This can’t happen as each string in the sequence is made up of bits of length 2 numbers (number of/number) and it is impossible for two adjacent bits to be of the same number.

  5. I actually prefer an alternate version…

    The interesting thing is that it eventually becomes self-referential.

  6. Judging by the small number of comments compared to other puzzles I guess that not many people got the answer. That would include me as I haven’t the foggiest what’s going on despite having a B.Sc. in Mathematical Sciences. Mind you I am very very rusty as it was 20 years ago now. I wasn’t that good either but I enjoyed it none the less.

  7. This reminds me of

    Not hard to predict what comes next but a little harder to what generates them.

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