On Friday I posted this puzzle…. 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, ??

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

It’s easy – the sequence contains words that do not have the letter ‘E’ in them – that’s why it is called an Eban series.  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.

30 comments

  1. In Dutch:
    Twee, Vier, Zes, Dertig, … Veertig,
    They very much contain an E…

    And Richard didn’t answer his own question “can you figure out the next number in the sequence”? He probably meant 50 (which in this case works in Dutch too: Vijftig)

    1. I also found that in Dutch there is much more E.

      For example, thousand is “ebanned”, but the Dutch “duizend” is not. This makes the Dutch sequence very much shorter.

    2. The puzzle was presented in ENGLISH and requires the numbers to be written out in ENGLISH.

      I don’t see any mention of Dutch (or indeed any other language) in the puzzle, so why comment about the solution not working in a language that was never referenced in the puzzle? It works fine as presented.

      And, of course, I agree that Richard should have read his question and given the next in the sequence (50) as the answer before defining the sequence as an explanation.

    3. “For example, thousand is “ebanned”, but the Dutch “duizend” is not. This makes the Dutch sequence very much shorter.” How can an infinite number sequence be shorter than another infinite number sequence?

    4. Mathematics is simply more appealing when it applies universally, wouldn’t you agree?

      Language puzzles can be immensely enjoyable, but are prone to misunderstandings, even in English.

      Jules: What country are you from?
      Brett: What? What? Wh – ?
      Jules: “What” ain’t no country I’ve ever heard of. They speak English in What?
      Brett: What?
      Jules: English, mother***, do you speak it?

    5. “How can an infinite number sequence be shorter than another infinite number sequence?”

      Aleph numbers. Aleph 0 is infinity long, but still shorter than an aleph 1 sequence (e.g. ordinal numbers vs. real numbers)

  2. The German version seems somewhat short:

    5 (fünf)
    8 (acht)
    12 (zwölf)
    20 (zwanzig)
    25 (fünfundzwanzig)
    28 (achtundzwanzig)
    50 (fünfzig)
    55 (fünfundfünfzig)
    58 (achtundfünfzig)
    80 (achtzig)
    85 (fünfundachtzig)
    88 (achtundachtzig)

  3. Reminds me of the book „La Disparition“ of Georges Perec
    it is even an eban book…

    compared thereto these few numbers are just child’s game…

    going to file it under futile information

  4. Still, as a non-native English speaker, I always feel a little bit disappointed (and in disadvantage) when a puzzle is presented which *seems* to be about mathematics, logic and reason, but turns out to be about *english language*, logic and reason 😉

  5. Although I have to admit that such kind of puzzles are presented frequently, so at least I don’t feel suprised anymore if it happens
    8-D

  6. “The sequence contains words that do not have the letter ‘E’ in them” – well, no number I write has an ‘e’ in it, they all have digits.

    In any case, by that rule, the next in the sequence is ‘turnip’

  7. With the following function
    f(x)=2.5x-mod(x/2;2)+30-abs(5x-mod(5x;20)-30)
    The sequence f(x) can be fitted to x-values of 1-11, with the next number being f(12).

    In this manner, the next number is 30.
    No need to solve this linguistically, math is always there 😉
    In other words I didn’t solve it.

  8. Allows me to presents yous with the zBan sequence.

    It start at one (cleverly, that’s just after zero).

    And goes on up forever.

    Or at least until boredom creeps in, and you declare the nex number to be one zillion.

    A simple sequence, yet one that contains so much.

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