It’s the Friday Puzzle!


A simple one this week.  Mathematicians often refer to the following list of numbers as an ‘Eban’ sequence – without looking up that term, can you figure out the next number in the sequence?

2, 4, 6, 30, 32, 34, 36, 40, 42, 44, 46, ??

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.


41 comments on “It’s the Friday Puzzle!

  1. Not a native english speaker says:

    I could not get it, beacuse I though it mathematicaly. So I checked it . So funny…

  2. Anonymous says:

    1 min. Though I doubt they’re real mathematicians.

  3. Michael Sternberg says:

    Hmm, after a couple of minutes I decided I have one digit of the solution and not enough entropy to decide the other among a couple plausible solutions.

    BTW, going by the letter of the instructions, one might be permitted to look up the sequence itself …

  4. Drew says:

    30 second job because i’ve learn now not to jump in with the maths and to read the questions more intently

  5. John Loony says:

    In Volapük the sequence would start 1, 3, 4, 5, 6, 8, 9, 100, 101, 103 etc.

    In Esperanto it starts 1, 2, 3, 4, 5, 8, 9, 1000, 1001, 1002, 1003, 1004, 1005, 1008, 1009, 2000, 2001 etc.

    In Arabic it includes all integers.

  6. Nigel Alexander says:

    couldn’t get till I read the comments!

  7. Goliath says:

    Like that riddle. Much better than the one last week. Writing down the sequence helps…

  8. John Read says:

    I have a sense that if there were a 0 before the first 2 then there would be a different answer.

  9. Anataboga says:

    About 30 seconds. Then checked with google and gave myself a tick.

  10. Bleach says:

    In the netherlands, I believe would be the 8th number in the list.

  11. Anonymous says:

    I will never tell you guys that there is a database of integer sequences called “The On-Line Encyclopedia of Integer Sequences” and can be found here:

  12. Waddett says:

    Couldn’t get it so cheated and looked up on google.
    Now have sore leg from where I kicked myself.

  13. Andy says:

    Got it by the wrong means. I guess I guessed.

    • AMWhy says:

      To be pedantic, I reckon my answer is about 3.8 lower than everyone else…
      I have to say, I looked up the term and while it’s clever, I was disappointed. Being a maths degree holder and never hearing of this before I expected something a little more mathematical.

  14. Lazy T says:

    Holding strictly to axiom, you can’t say ‘a sequence of numbers, or integers, or terms’. How about a list of things?

  15. wraakh says:

    Swedish: 2,4,7,8,9,10,12,14,17,18,20,22,24,27,28,29

  16. Camel Ali says:

    Yup. Got it. Keen to see how many people come up with alternative answers this week.

  17. David Hanley says:

    I had a simple mathematical rule that turned out not to be the answer richard was looking for.

  18. MC says:

    A better puzzle might have been to take this to the 14th term, and ask for the next… The second and rather intriguing jump in the numbers…

  19. Scifind says:

    Got it right in 10 seconds, for the wrong reason, doh.

    • Todio says:

      Same here. Had it almost before I read the question then looked it up and was right but my reasoning would have fell apart after another couple of iterations.

  20. mittfh says:

    OK, I had to look it up, then realised the significance of the term…

    Meanwhile, since we’re covering different languages, to the best of my understanding, to a Welsh speaker the first few would be:

    1, 2, 3, 5, 7, 8, 9, 20, 21, 22, 23, 25, 27, 28, 29

    Depending on who you ask, the next number in the sequence could be either 60 or 100…

  21. Mickey D says:

    Had to look it up… Great!

  22. Emlyn says:

    1, 3, 5, 6, 8, 10, 18, 20, 23, 25, 26, 28, 1000000, …

    1, 2, 4, 5, 8, 1000, 1001, 1002, 1004, 1005, 1008, …

    I think, I could have made a mistake in there…

  23. Ophelia Balls says:

    Solved in 0.0000000000000000056 seconds

  24. Luisa says:

    portuguese: 1, 2, 4, 5, 8, 1000, 2000, 4000, 5000, 8000, 30000… and then the billions

  25. flatlander :-( says:

    I got it straight away, like not even a second. Then I looked it up (because I had never heard of such a thing) and found out that
    A- I was right in the next number AND
    B- I had no reason to be correct other than dumb luck, because I had no idea why that would be the next number other than my mathematically challenged brain thought it sounded good.

    Still, I claim victory!

  26. GB says:


  27. Jerry says:

    Score one for mathematicians!

  28. Mmm… Got it in less than 30 seconds. Just from the name, which reminded me of E-Prime.

  29. Kristian says:

    I found a rather short mathematical expression that fits this sequence exactly and through it I’ve found a candidate for the 12th number. Obviously it’s not the solution, but hey…

  30. Anonymous says:

    i know what the next one is and i did check it out and i did get the right answer but i also thought it was a math pattern.but i was mistaken :/ it was still fun and it took a few seconds

  31. zackapeng says:

    In German I think it’s:
    8 20 28 80 88 800 808 820 828 888 …

    If im not missing anything. Didnt got it without looking.

  32. Anonymous says:

    Should it not read INTEGER rather than NUMBER. Otherwise the sequence would never get past 2.2222222222(recurring)


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