It’s that time again!  OK, here is the puzzle…..what number comes next in the sequence?

1    4    7    11    15    19

Clue: It is less than 19.

As ever, please do NOT post your answers, but do say if you think you have solved the puzzle and how long it took.  Solution on Monday.

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 think I’ve got it, but I’m a little confused. As far as I can tell, the next number in the sequence doesn’t HAVE to be less than nineteen, it could be one of several options. If it HAS to be less than 19, then, by my figuring, the third number in the sequence should be three, not 7.

    Or have I just got the wrong rule?

    1. I might clarify after reading more comments, it does not need to be a unique sequence, as long as ever number fulfils the rule then the sequence is maintained. It would only be a problem if there was more than one allowable answer.

  2. Couple of minutes, although to be consistent with the clue some of the earlier numbers in the sequence should be different.

  3. I agree. If we said that in all cases where there’s a choice that one goes for the lowest option it would make it more logical. So, next question – how long does the sequence go on before you can’t continue it?

    1. it’s a sequence, it doesn’t have to be a unique sequence. The point is that there is only one number under 19 that fulfils the conditions.

  4. I’m reasonably sure I found the same answer as Carl. Noticed the pattern early on, found what I thought was the answer, double checked it an found that the 7 did not completely match the pattern as defined by the clue.

    So, if is the answer, I got it in under 5 minutes. Might continue to look.

    1. Yes, I have that issue too. The 7 is not really correct. There is a better number in that position. Same thing for the 19.

  5. I believe I have the answer. In fact I have two possibles, but am working on the premise that the correct one is the lower of the two. It took 5 mins or so.

  6. In less than a minute I found one solution, but my definitons are loose. ie it doesn’t have to start with 1, 4 (and as Mathlete says it could be 13 instead of 19) – and there are answers above 19 I’ve found too!

  7. I’ve been baffled by one of these in the past that ran in the same vein. It made my brain hurt. Thankfully I am on the lookout for them now so this one only took a minute to solve.

  8. Anyone else feel like we’re not really getting puzzles anymore, just math problems? Could do with changing it up a bit, getting bored now…

  9. I have what seems to be a correct answer, but I can’t use that answer and the given sequence to infer deterministic rules for constructing the sequence. So I’m either wrong or disappointed (or missing a key detail of the given sequence).

  10. Here’s my variation, for which the series is unique:
    1 4 3 11 15 13 __
    I think this is what many of the other commenters were getting at.

    1. Yes. We’ve clearly all got the same answer and reason, but the clue actually forces you to go for an answer that’s less consistent with the rest of the sequence than one you might otherwise choose. For me, it makes more sense if either the sequence is as you say, or the answer is greater than 19.

    2. I think I got it, if my guess is correct, this puzzle is amusing…..when the solution first came to my mind, i thought it is ridiculous but when I wrote it down, it proved my hypothesis!
      Here is my variation

      the limitation is nessesary
      2 5 3 8 12 16 13 ____ 24 28………

  11. I got the pattern immediately (I guess my brain is just working that way today) and it just took a few more seconds to figure out the right number. I think the clue probably helped.

  12. If we have got the right idea then definitely 13 would replace 19. May be we haven’t. Surely RW wouldn’t have made a mistake?

  13. I may be completely missing something here (very likely) but if you are going and changing numbers in the sequence then it isn’t really the same sequence or same rules.

    That said I’ve never been good at this sort of puzzle.

  14. i do not believe numbers have “sequences” that they can be put in. numbers want to be free, and i for one will not attempt to ensalve them

  15. I think the reason not 3 or 13 used is to make a sequence that increases. That would be the puzzle to which there might be more than one answer. The clue is a clever way of both ensuring only one answer and also being a pointer to how to solve it (usually the sole purpose of a clue). Some commenters have too pedantic and narrow-minded an approach to these puzzles which as well as being annoying, portrays them as boring “wet blankets”. (In my opinion)

  16. today I managed to do it. As for the not univocal solution, the simplest thing would have been to use every time the least number under the rule.

  17. About a minute. I’m curious as to why you chose 7 and (instead of 3) and 19 (instead of 13). You wouldn’t have had to point out that the answer would be less than 19, because order wouldn’t have mattered. Unless you wanted to throw us off with the fact that most of the numbers are separated by 4.

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