On Friday I set this puzzle…..Here is a series of numbers, starting with the number zero.  What is the hidden logic in the series and why can’t it be continued?

0, 1,  8,  10,  19,  90

If you have not tried to solve it, have a go now.  For everyone else the answer is after the break.

Each number in the series begins with the last letter of the previous number.  So,it runs

ZERO, ONE, EIGHT, TEN, NINETEEN, NINETY…

There is no number starting with Y, so that is the end of the series.

Did you solve it?  Any other solutions?

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. Roland says:

Yotta (10^24), Atto (10^-18), One, Eight, …

1. cozdas says:

Nice try 🙂

Yotta and Atto are prefixes for units, not numbers and they are not numbers themselves. Kilo is not a number, one thousand is.

2. David D says:

Good puzzle (I didn’t get it!)

3. Chris Emerson says:

Surely you need to specify that each number should be the lowest number that meets the requirement which is more than the previous number. Otherwise you could have

1 81 81 81 81 81 109 872 1 81 8 etc…

1. JohnF says:

Exactly. The pattern/rule is not just that the start/end letters must match but that the next one in the sequence must be higher than the current number but also be the lowest of all the possibles that fit that criterion.
In short… what will generate all and ONLY ALL of the sequence given so far. Otherwise there could be many answers and to pick the “right” one resorts to a guessing game.

2. tort says:

No you don’t. You don’t need that requirement to solve the puzzle, it’s irrelavent that the rule could produce other numbers in the series.

3. Caper says:

Agree with Tort; question doesn’t request anything other than :”What is the hidden logic in the series….”.. It’s saying that a series of numbers is as shown, and why??

4. Tort / Caper- By your logic the answer could be “each number is bigger than the one before it”. It holds for the given sequence, but it’s not the answer because there’s a more restrictive rule which generates the sequence.

5. Vince says:

Thomas that would not work because he also ass why the series can’t be continued. You just left that part out of your whole each number is bigger than the last counterargument.

6. Substitute “each number is bigger than the one before it, and strictly less than 91” for “each number is bigger than the one before it” in my post then. My logic still holds.

We’re looking for the most restrictive & simple rule that explains the sequence and why it can’t be continued. The requirement that it’s the *next lowest number* starting with the letter the last one ended with is more restrictive than simply starting with the letter the last one ended with, so that’s the answer we’re looking for.

4. A tricky one…I am sure that not many got that one !! I certainly didn’t.

The series could have been shortened to
0, 1, 18, 90

or alternatively
0, 1, 80

or
1, 80

1. rmb says:

or
80

5. Anders says:

Damn, I thought it would be something “meta” like this, but I didn’t quite reach it. Oh well

6. SereneBlueSky7 says:

Damn, I didn’t solve this after all! I thought it like this:
0, 1, 8, 10, 19, 90

0+1+8+10=19 and looking at the numbers I saw first 0,1 ie. 01 and 8 between 10 and 01.
I thought it was a sort of sequence where the 0 is the first and 1 the second and then 8 and 9 added in between them. And they do also add up together to be 19. I must admit the final 90 was a bit of a problem, but I guess I thought the sequence changes there a bit and now takes the last number of the previous figure to be the first one before 0 and then 0 ending the sequence making it a circle. 🙂 Oh yeah, I’m logical.

7. SereneBlueSky7 says:

In my language the sequence would’ve been naturally impossible.

Nolla, yksi, kahdeksan, kymmenen, yhdeksäntoista, yhdeksänkymmentä 🙂

“There is no number starting with Y”

Yes, there are, plenty! Yksi (1), yhdeksän (9), yhdeksäntoista (19), yhdeksänkymmentä (90).

1. Julia says:

It seems to me that the problem with Finnish is that there are no numbers starting with a vowel. So the sequence would be
0
and that’s it.

8. Julia says:

I like puzzles where reading the question carefully gives you a clue towards the answer. In this case it was the phrase “starting with the number zero”. Why mention zero specifically, when it is clear from the number sequence anyway? I got the answer very quickly after asking myself that question.

1. Indeed, a series starting at nought or nil would be very different!

I didn’t get it this week, should have spotted the clue.

2. Lazy T says:

Agreed, I started thinking oh one eight and got nowhere. It took a second look on saturday to realize zero was key.

9. It’ s nice to see how it works in other languages (like Finnish, above).

In Spanish there is little interest: 0 (cero), 11 (once)

It gets a little better starting with 2: 2 (dos), 6 (seis), 60 (sesenta)

10. Waldo says:

Did not get it, and was not on the right track when I gave up.

11. I tried yesterday and didn’t get to the solution until I gave up and decided to see the answer today. Now, just before clicking the post to see the answer, I felt bad for giving up and tried again. Solved now, on the last minute and confirmed my answer. This made me happy today =)

12. Michael Sternberg says:

Didn’t get it.

Gotta say, I’m not fond of puzzles that look like abstract and universal math but whose solutions depend on spelling in a specific language. Of course, over here, I should’ve known better 🙂 So, better add check spelling to the repertoire, alongside Roman and upside down.

13. spiderabc1 says:

I didn’t get it. Tried not to think about it. Thought about 1+8=9 etc and what with another 0 in the middle and end, but gave up as I was going down the wrong route.

14. MarKill says:

if you always start with 0 then in Dutch you wouldn’t go further then that as that is nul and no number starting with an l in Dutch

15. You could make the Spanish work with some massaging, but it gets a little 6-centric

2, 6, 62, 63, 66, 602, 603, 606, and so on.

16. Actually, you could work in 8s too. 66, 68, 83, say.

17. Jon d says:

I didn’t solve it and wasn’t close to being on the right track, I might have done if I’d used a pencil and paper. Suppose my brain processes numbers as numbers and not words unless I’m writing a cheque – which I’ve not done in several years now come to think of it.

18. Holden Caulfield says:

Must be running out of ideas, that was dreadful, it could have read 0, 1, 85, 8, 10, 9,000,000, 19, 90 and made as much sense.

I doubt this is going to boost the book sales, and that’s what it’s all about isn’t it?

19. Jerry says:

I got this one, although it took a bit of sloshing around in my head over the weekend to see it.

20. SeleneBlueSky7 says:

Julia,

Y is a vowel in Finnish. I thought it’s a vowel in English as well.
It just happens to be the only vowel with which any number words start.
This is the sequence up to ten in my lang:
Y, K, K, N, V, K, S, K, Y, K.

K dominating the game. 🙂

1. Julia says:

yes, but as far as I know there are no numbers ending in y, so the sequence doesn’t work. Please correct me if I am wrong – I can only count to ten in Finnish.

The longest sequence I can think of is 7 (or 8, 9 or 10) followed by 0 or 4.

21. SeleneBlueSky7 says:

Julia,

Yeah, no number words ending in Y in my language. The usual letters ending number words in Finnish are probably I and N anyway. Overall Finnish word endings are more vowels than consonants, except N…or T in plurals.
1, 2, 5, 6 all end in I in Finnish. 7,8,9,10 end in N.

22. Camel says:

Didn’t get this one. Well done to all that did.

23. Marion says:

I didn’t get this at all, obvious when you know but never mind.

24. Ditto to Ginny re: posting the earlier letters for new subscribers. Alsocan you inform us who wrote the January letters?