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Posers and Puzzles

Posers and Puzzles

  1. Standard member Crowley
    Not Aleister
    13 May '03 21:54
    I saw this on another site, pretty good one...

    What row of numbers comes next?
    1
    11
    21
    1211
    111221
    312211
    13112221
    ..........
  2. Standard member godzillion
    (dandan)
    13 May '03 23:23
    Originally posted by Crowley
    I saw this on another site, pretty good one...

    What row of numbers comes next?
    1
    11
    21
    1211
    111221
    312211
    13112221
    ..........
    1113213211
    ...but I won't say why.
  3. Standard member Toe
    14 May '03 12:29
    Originally posted by godzillion
    1113213211
    ...but I won't say why.
    and the row after that is
    31131211131221

    seems this is a well known one (1?)
  4. 14 May '03 12:40
    Originally posted by Toe
    and the row after that is
    31131211131221

    seems this is a well known one (1?)
    ... followed by 13211311123113112211

    Mick
  5. Standard member jot
    14 May '03 18:37
    Here's some more:


    1 ;1
    11 ;2
    21 ;2
    1211 ;4
    111221 ;6
    312211 ;6
    13112221 ;8
    1113213211 ;10
    31131211131221 ;14
    13211311123113112211 ;16
    11131221133112132113212221 ;22
    3113112221232112111312211312113211 ;30
    1321132132111213122112311311222113111221131221 ;42

    The sequence on the right is the amount of digits in each row. Can anyone fit a formula to that series?
  6. Standard member royalchicken
    CHAOS GHOST!!!
    14 May '03 19:02
    Just a guess: each term describes the number of times each digit appears in the previous term, with the exception of the first term, which is defined as 1?

    1
    11 (one one)
    21 (two ones)
    1211 (one two, one one)
    111221 (one one, one two, two ones)
    ...
    Interestingly, I don't think it is possible to ever get a four to appear here. Does that sound right?
  7. Standard member Crowley
    Not Aleister
    14 May '03 21:18
    Originally posted by royalchicken
    Just a guess: each term describes the number of times each digit appears in the previous term, with the exception of the first term, which is defined as 1?

    1
    11 (one one)
    21 (two ones)
    1211 (one two, one one)
    111221 (one one, one two, two ones)
    ...
    Interestingly, I don't think it is possible to ever get a four to appear here. Does that sound right?
    Hmm, too easy
    I don't know about a four coming up, but looking at the other posts, it doesn't seem that it'll appear in a row.
  8. Standard member royalchicken
    CHAOS GHOST!!!
    14 May '03 22:33
    Thanks...actually, think about what happens when 3 ones show up in a sequence and you can tell why there can't be a four.
  9. Standard member royalchicken
    CHAOS GHOST!!!
    15 May '03 19:00
    In fact, note that any three digit sequence in a term becomes a two digit one in the next term, two digits ones become two-digit ones, and one digits ones become one-digit ones. So if you know the relative frequencies of one-, two-, and three-digit blocks you can find an easy asymptotic estimate of the number of digits in the nth term...any guesses here? I'll tell you if you're right...