Posers and Puzzles

Posers and Puzzles

  1. Germany
    Joined
    27 Oct '08
    Moves
    3118
    03 Mar '10 13:113 edits
    What is the next number in the following sequence?

    0
    1
    2
    2.60121894356579510020490322708104361119152187501694... x 10^1746 (approximation)
  2. Standard memberwolfgang59
    Mr. Wolf
    at home
    Joined
    09 Jun '07
    Moves
    46110
    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. Germany
    Joined
    27 Oct '08
    Moves
    3118
    04 Mar '10 07:17
    Originally posted by wolfgang59
    42 (approximation)
    42 is not the answer!
  4. Joined
    26 Apr '03
    Moves
    26588
    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. Subscriberjoe shmo
    Strange Egg
    podunk, PA
    Joined
    10 Dec '06
    Moves
    7733
    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. Germany
    Joined
    27 Oct '08
    Moves
    3118
    04 Mar '10 20:56
    4!!!! is the correct answer.

    Or written alternatively: 10^(10^(10^25.16114896940657)).
  7. Joined
    11 Nov '05
    Moves
    43938
    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. Subscriberjoe shmo
    Strange Egg
    podunk, PA
    Joined
    10 Dec '06
    Moves
    7733
    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. Germany
    Joined
    27 Oct '08
    Moves
    3118
    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. Joined
    26 Apr '03
    Moves
    26588
    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.
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