On Friday I set this puzzle…..

What row of numbers comes next?1

11

21

1211

111221

312211

13112221

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

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.
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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!

Reblogged this on thepositivevoice.

Easy!

Nailed it. I never saw this one before either.

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.

Well amazing

Who didn’t get the answer?

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

base 4?

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

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.

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.

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.

i read it on monday, and i found the answer even before considering clicking “continue reading”..

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

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.

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.

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

I actually prefer an alternate version…

1

11

21

1211

1231

131221

132231

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

That is pretty cool.

Nice puzzle.

One-One was a racehorse,

Two-Two was one too.

One-One won one race,

And Two-Two won one too.

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.

This reminds me of

1

121

12321

1234321

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

oh, in my country, the question’s order is opposite.

like this :

11

12

1121

…