## counter ex. for 46; Ramsey Numbers

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• 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
• 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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