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counter ex. for 46; Ramsey Numbers

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  • Bill Bouris
    Pete, I did it by hand; sorry for the intrusion, last time. the counter-example for 46; 45 is not enough! notice how the columns are formed; that s how I m
    Message 1 of 2 , Jan 27, 2010
      Pete, I did it by hand; sorry for the intrusion, last time.

      the counter-example for 46; 45 is not enough!

      notice how the columns are formed; that's how I'm able
      to find the counter-example. if BABBB were 10111, then
      it would equal 23 decimal; and 23 divides 46.

      column one: every other on/off
      column two: two on, two off
      column three: four on, four off
      column four: six on, six off
      last column: split as best possible

      AAAAA   BABBB
      BAAAA   AABBB
      ABAAA   BBBBB
      BBAAA   ABBBB
      AABAA   BAABB
      BABAA   AAABB
      ABBBA   BBAAB
      BBBBA   ABAAB
      AAABA   BABAB
      BAABA   AABAB
      ABABA   BBBAB
      BBABA   ABBAB
      AABAA   BAABB
      BABAA   AAABB
      ABBAA   BBABB
      BBBAA   ABABB
      AAAAA   BABBB
      BAAAA   AABBB
      ABABA   BBBAB
      BBABA   ABBAB
      AABBA   BAAAB
      BABBA   AAAAB
      ABBBB   BBAAA
      BBBBB   ABAAA
      AAAAB   BABBA
      BAAAB   AABBA
      ABAAB   BBBBA
      BBAAB   ABBBA
      AABAB   BAABA
      BABAB   AAABA
      ABBBB   BBAAA
      BBBBB   ABAAA
      AAABB   BABAA
      BAABB   AABAA
      ABABB   BBBAA
      BBABB   ABBAA
      AABAB   BAABA
      BABAB   AAABA
      ABBAB   BBABA
      BBBAB   ABABA
      AAAAB   BABBA
      BAAAB   AABBA
      ABABB   BBBAA
      BBABB   ABBAA
      AABBB   BAAAA

      both sets together offer total randomness, but the right set doesn't
      guarantee an 'all off' setting!; i.e. A=off, B=on; otherwise, you can
      find... AAAAA, AAAAB, AAABA, etc. It shouldn't be a millenium
      project... just one to help people to learn to count.

      Bill
    • Bob Gilson
      Isn t it amazing that a Swedish pop group can have so much influence! ________________________________ From: Bill Bouris To: Peter
      Message 2 of 2 , Jan 29, 2010
        Isn't it amazing that a Swedish pop group can have so much influence!



        ________________________________
        From: Bill Bouris <leavemsg1@...>
        To: Peter Kosinar <goober@...>; pgroup <primenumbers@yahoogroups.com>
        Sent: Wed, January 27, 2010 5:02:47 PM
        Subject: [PrimeNumbers] counter ex. for 46; Ramsey Numbers


        Pete, I did it by hand; sorry for the intrusion, last time.

        the counter-example for 46; 45 is not enough!

        notice how the columns are formed; that's how I'm able
        to find the counter-example. if BABBB were 10111, then
        it would equal 23 decimal; and 23 divides 46.

        column one: every other on/off
        column two: two on, two off
        column three: four on, four off
        column four: six on, six off
        last column: split as best possible

        AAAAA BABBB
        BAAAA AABBB
        ABAAA BBBBB
        BBAAA ABBBB
        AABAA BAABB
        BABAA AAABB
        ABBBA BBAAB
        BBBBA ABAAB
        AAABA BABAB
        BAABA AABAB
        ABABA BBBAB
        BBABA ABBAB
        AABAA BAABB
        BABAA AAABB
        ABBAA BBABB
        BBBAA ABABB
        AAAAA BABBB
        BAAAA AABBB
        ABABA BBBAB
        BBABA ABBAB
        AABBA BAAAB
        BABBA AAAAB
        ABBBB BBAAA
        BBBBB ABAAA
        AAAAB BABBA
        BAAAB AABBA
        ABAAB BBBBA
        BBAAB ABBBA
        AABAB BAABA
        BABAB AAABA
        ABBBB BBAAA
        BBBBB ABAAA
        AAABB BABAA
        BAABB AABAA
        ABABB BBBAA
        BBABB ABBAA
        AABAB BAABA
        BABAB AAABA
        ABBAB BBABA
        BBBAB ABABA
        AAAAB BABBA
        BAAAB AABBA
        ABABB BBBAA
        BBABB ABBAA
        AABBB BAAAA

        both sets together offer total randomness, but the right set doesn't
        guarantee an 'all off' setting!; i.e. A=off, B=on; otherwise, you can
        find... AAAAA, AAAAB, AAABA, etc. It shouldn't be a millenium
        project... just one to help people to learn to count.

        Bill




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