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Posers and Puzzles

Posers and Puzzles

  1. 03 Mar '10 13:11 / 3 edits
    What is the next number in the following sequence?

    0
    1
    2
    2.60121894356579510020490322708104361119152187501694... x 10^1746 (approximation)
  2. Standard member wolfgang59
    Infidel
    03 Mar '10 22:22
    Originally posted by KazetNagorra
    What is the next number in the following sequence?

    0
    1
    2
    2.60121894356579510020490322708104361119152187501694... x 10^1746 (approximation)
    42 (approximation)
  3. 04 Mar '10 07:17
    Originally posted by wolfgang59
    42 (approximation)
    42 is not the answer!
  4. 04 Mar '10 20:00
    Hmm, the answer seems to depend on whether the sequence is:

    1!
    2!!
    3!!!

    or
    1!!!
    2!!!
    3!!!

    which give the same answers up to the third value, which is all we have.
  5. Subscriber joe shmo
    Strange Egg
    04 Mar '10 20:08
    Originally posted by iamatiger
    Hmm, the answer seems to depend on whether the sequence is:

    1!
    2!!
    3!!!

    or
    1!!!
    2!!!
    3!!!

    which give the same answers up to the third value, which is all we have.
    the 0 in the sequence gives the solution

    cant be 0!!! =1, thus the first term must be zero

    so

    0
    1!
    2!!
    3!!!
    4!!!!

    nice catch
  6. 04 Mar '10 20:56
    4!!!! is the correct answer.

    Or written alternatively: 10^(10^(10^25.16114896940657)).
  7. 04 Mar '10 21:10
    Originally posted by KazetNagorra
    4!!!! is the correct answer.

    Or written alternatively: 10^(10^(10^25.16114896940657)).
    A good one!

    I just thought the problem as silly at first, but now I enjoy the problem, and its solution!
  8. Subscriber joe shmo
    Strange Egg
    05 Mar '10 00:06
    Originally posted by KazetNagorra
    4!!!! is the correct answer.

    Or written alternatively: 10^(10^(10^25.16114896940657)).
    Is there a general series definition for this? I tried to develop one but my head exploded.

  9. 05 Mar '10 07:23
    Originally posted by joe shmo
    Is there a general series definition for this? I tried to develop one but my head exploded.

    I have no idea, this is just what Wolfram Alpha gave me.
  10. 09 Mar '10 01:03
    Originally posted by KazetNagorra
    I have no idea, this is just what Wolfram Alpha gave me.
    Looking at: http://en.wikipedia.org/wiki/Factorial

    Wolfram may be using the equation given under "multifactorials", which uses k as "the number of exclamation marks.