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Re: A number game

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  • video_ranger
    Some of the rules are a little ambiguous - could you give an example? 1, 6, 1, 8, 0, 3, 3, 9, 8, 8, 7, 4, 9, 8, 9, 4, 8, 4, 8, 2, 0, ... -- ?
    Message 1 of 3 , Jan 22, 2013
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      Some of the rules are a little ambiguous - could you give an example?

      1, 6, 1, 8, 0, 3, 3, 9, 8, 8, 7, 4, 9, 8, 9, 4, 8, 4, 8, 2, 0, ...
      -->
      ?


      --- In mathforfun@yahoogroups.com, "bjornaltrecht" wrote:
      >
      > Here are the rules as I understand them.
      >
      >
      > Take a decimal expansion of an irrational number (phi is optimal).
      > Digits 0 mod 3 are "angry numbers"
      > Didits 1 mod 3 are "male numbers"
      > Digits 2 mod 3 are "female numbers"
      >
      > 0's are dropped from the number string
      >
      > Rules;
      > Digits >6 can't do anything
      > Angry numbers affect the leftmost digit.
      > An angry digit next to a male digit reduces the male digit by 2
      > An angry digit to the right of a female digit reduces the angry digit by 1
      > A male and a female digit produce a 1 to the right of both of them.
      > This happens for each iteration of the rules toward a number. After this iteration, all the the digits are increses\d by one and the zeroes are dropped and the game continues..
      >
      > is there ever a finality or a fixed point for this game?
      >
      > thank you all for having me to this group
      > bjorn
      >
    • bjornaltrecht
      A friend showed me this game a long time ago, but I think I messed up with a few of the rules. The numbers 1, 4 and 7 are male numbers; The numbers 2, 5 and 8
      Message 2 of 3 , Jan 29, 2013
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        A friend showed me this game a long time ago, but I think I messed up
        with a few of the rules.

        The numbers 1, 4 and 7 are male numbers;
        The numbers 2, 5 and 8 are female numbers;
        The numbers 3, 6 and 9 are angry numbers.

        You are given the decimal expansion of any rational number and start
        on the leftmost digit. This is actually a computer algorithm task.


        The rules


        1)Zero's are dropped out of the string as you come to them.

        2)As you scan from the left, a male and a female number produce a 1 digit to the right. Scan one digit past the offspring.

        3)If an angry number is next to a male number either 4 or 7, then take two away from the male number then scan past the angry number.

        4)If a female number is next to an angry number, then the angry number is dropped from the string. Scan past the female number and repeat all steps.

        Scan past pairs of like numbers until a step can be taken.

        When the left digits are no longer affected, then increase each digit by 1 and then mod 9 and then repeat all the rules.

        My friend said that eventually the rules would be exhausted and that the result would be nothing but like pairs of numbers.

        Using the digits of Phi as an example;

        16->16
        161->161
        1618->16181
        161810->16181
        1618183->161818
        1618183->161818
        1618189->161818
        1618188==same
        16181888==same
        161818887->1618188871
        16181888714==same
        161818887149->161818887129
        1618188871298->161818887128
        the resulting string so far when continued is
        16188871284814812...

        Then increase all the digits by one and repeat.
        The new string would be
        27299982395925923...
        Note that in the new string, there are no zeros or ones. All males become female. All females became angry. Any angry numbers in the first string that remained become the only males in this new string.
        In this new string all angry numbers will be dropped.
        By the third string, there are no males
        By the fourth string, you get nothing but angry numbers


        --- In mathforfun@yahoogroups.com, "video_ranger" wrote:
        >
        > Some of the rules are a little ambiguous - could you give an example?
        >
        > 1, 6, 1, 8, 0, 3, 3, 9, 8, 8, 7, 4, 9, 8, 9, 4, 8, 4, 8, 2, 0, ...
        > -->
        > ?
        >
        >
        > --- In mathforfun@yahoogroups.com, "bjornaltrecht" wrote:
        > >
        > > Here are the rules as I understand them.
        > >
        > >
        > > Take a decimal expansion of an irrational number (phi is optimal).
        > > Digits 0 mod 3 are "angry numbers"
        > > Didits 1 mod 3 are "male numbers"
        > > Digits 2 mod 3 are "female numbers"
        > >
        > > 0's are dropped from the number string
        > >
        > > Rules;
        > > Digits >6 can't do anything
        > > Angry numbers affect the leftmost digit.
        > > An angry digit next to a male digit reduces the male digit by 2
        > > An angry digit to the right of a female digit reduces the angry digit by 1
        > > A male and a female digit produce a 1 to the right of both of them.
        > > This happens for each iteration of the rules toward a number. After this iteration, all the the digits are increses\d by one and the zeroes are dropped and the game continues..
        > >
        > > is there ever a finality or a fixed point for this game?
        > >
        > > thank you all for having me to this group
        > > bjorn
        > >
        >
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