# Answer to the Friday Puzzle….

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On Friday I set this puzzle…..

What row of numbers comes next?1
11
21
1211
111221
312211
13112221
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
1113213211

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

One One
Two Ones
One Two One One
etc.

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. Appocomaster says:

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. Reblogged this on thepositivevoice.

3. Mickey D says:

Easy!

4. Merari says:

Nailed it. I never saw this one before either.

5. Ben Saunders says:

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.

• Sanjana says:

Well amazing

Am I the only one who over thought it and tried converting each line from base-3 to base-10?

• Eddie says:

base 4?

Oh, zero! Good point. Even if that had been the solution I wouldn’t have got it 🙂

• Ronda says:

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.

7. Andy says:

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.

• Steve S says:

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.

8. Berhard says:

9. The other Matt says:

I tried to solve it by watching it graphically. When the rows are aligned it looks like a Tree.

10. Ken Haley says:

This is known as the “look-and-say” sequence. Credit for initial discovery and analysis goes to John Conway (who also invented the very popular computer game called “Life”). See http://en.wikipedia.org/wiki/Look-and-say_sequence.

11. Eddie says:

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.

12. Dharmaruci says:

i solved this differently by looking down the columns. it can have a 4!

13. James says:

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

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

• Eddie says:

That is pretty cool.

14. mightyhero says:

Nice puzzle.

15. jramills says:

One-One was a racehorse,
Two-Two was one too.
One-One won one race,
And Two-Two won one too.

16. Steve says:

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.

17. Steve says:

This reminds me of
1
121
12321
1234321

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

18. Hoeun says:

oh, in my country, the question’s order is opposite.
like this :
11
12
1121