Discover the Rule

Found the following cute puzzle on Facebook.

Puzzle. Discover the rule governing the following sequence to find the next term of the sequence: 8, 3, 4, 9, 3, 9, 8, 2, 4, 3.

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17 Comments

  1. Alex:

    6,7

  2. Blaine:

    …4,4,2,3,8

    That was fun!

  3. gabriella:

    …4,5,3,5,4,2,6,3,4,7,3,7,6,2,8,3,4,9…

  4. Leo B.:

    …,1,9,5,2,4…

  5. Robert:

    … 4, 6, 3

    but I’m not sure .. what is the reasoning behind?

  6. tanyakh:

    One of the five answers above is correct. Hint: The rule is simple. If you are not sure, you didn’t discover it.

  7. Michael:

    Blaine has it. Unfortunately I don’t see a way to determine additional terms… unless they are 1, 1, 1…?

  8. Blaine:

    Michael, perhaps it could continue as 5, 5, 4, 4, 5, 4, 5, 3… and would it eventually devolve into 4, 4, 4… ?

  9. Richard:

    Mmmh, I don’t follow

  10. tanyakh:

    Hint: This is a self-referencing puzzle.

  11. Leo B.:

    I got it; however, my very simple (and human language-independent!) program says 1,9,5,2,4.

    Indeed, the rational number with the lowest denominator, which decimal form starts with .8349398243 is 138681/166097 = 0.83493982431952413348…

  12. Stefano:

    …4,4,2,3,9(or 8) ?

  13. Cristóbal Camarero:

    I see the mirror rule a(i)=a(13-i)+1 for i<13-i, i!=4. This would continue with two terms: 2 and 7. But this is different to all given ones and Tanya said the good is already given.

  14. Blaine:

    Hint: ignore the word “Puzzle” and proceed from there.

  15. Cristóbal Camarero:

    Oh! I see now, nice. Not as much a self-referencing puzzle as a prelude-referencing one, I would say.

  16. Marnix:

    …8

    And perhaps a couple of 1’s if you’re so inclined 🙂

  17. Marnix:

    ..4, 4, 2, 3, 8.

    And perhaps a couple of 1’s if you’re so inclined… 🙂

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