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Topic: 4 colors problem
Replies: 86   Last Post: Mar 13, 2014 4:36 PM

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stumblin' in

Posts: 58
Registered: 3/3/14
Re: 4 colors problem
Posted: Mar 11, 2014 12:15 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Let 0,1,2,3 represent four distinct colors.
Find a paired subsets.
0 1
0 2
0 3
1 0
2 0
3 0
1 2
1 3
2 1
3 1
2 3
3 2

These 12 pairs of colors can be used to color any-sized map
as long as any combination of them follows 4-color theorem
such that "1 3 0 1" would be okay, while "1 3 3 0" would not.
Also applies to vertical pairs,
1 3
0 2 <-- works.

1 3
0 3 <-- doesn't work.

The computer can randomly pick any pair to fill in more countries
following the 4-color theorem.

The 12 pairs can also be used to confirm that the coloring on a map
follows the 4-color theorem since any such map would inevitably use the
12 pairs of color ordering shown above, following the horizontal and vertical conditions shown above. I'm sure this is nothing new to anyone here. It was kind of a new insight to me. (no one has hinted at using such a method)

The upside of this is that hundreds or even thousands of colorings on a map may be found depending on the size of a map.
The downside is, there's no doubt that even more advanced methods will come along making a method such as this obsolete and archaic in no time.





Date Subject Author
3/3/14
Read 4 colors problem
stumblin' in
3/3/14
Read Re: 4 colors problem
Brian Q. Hutchings
3/3/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
g.resta@iit.cnr.it
3/3/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
g.resta@iit.cnr.it
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
g.resta@iit.cnr.it
3/4/14
Read Re: 4 colors problem
magidin@math.berkeley.edu
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
Port563
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
Brian Q. Hutchings
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
Port563
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
Brian Q. Hutchings
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read there should be a noncomputer proof of 4CT, I agree
Brian Q. Hutchings
3/4/14
Read Re: 4 colors problem
g.resta@iit.cnr.it
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
Port563
3/4/14
Read Re: 4 colors problem
stumblin' in
3/5/14
Read Re: 4 colors problem
stumblin' in
3/5/14
Read Re: 4 colors problem
magidin@math.berkeley.edu
3/5/14
Read Re: 4 colors problem
stumblin' in
3/5/14
Read Re: 4 colors problem
magidin@math.berkeley.edu
3/5/14
Read Re: 4 colors problem
quasi
3/5/14
Read Re: 4 colors problem
stumblin' in
3/5/14
Read Re: 4 colors problem
magidin@math.berkeley.edu
3/5/14
Read Re: 4 colors problem
stumblin' in
3/5/14
Read Re: 4 colors problem
quasi
3/5/14
Read Re: 4 colors problem
magidin@math.berkeley.edu
3/5/14
Read also, what is the spatial analog
Brian Q. Hutchings
3/5/14
Read Re: 4 colors problem
stumblin' in
3/5/14
Read Re: 4 colors problem
magidin@math.berkeley.edu
3/5/14
Read Re: 4 colors problem
stumblin' in
3/5/14
Read Re: 4 colors problem
Brian Q. Hutchings
3/5/14
Read Re: 4 colors problem
Virgil
3/5/14
Read Re: 4 colors problem
stumblin' in
3/5/14
Read Re: 4 colors problem
stumblin' in
3/5/14
Read Re: 4 colors problem
stumblin' in
3/5/14
Read Re: 4 colors problem
stumblin' in
3/5/14
Read Re: 4 colors problem
stumblin' in
3/5/14
Read Re: 4 colors problem
stumblin' in
3/5/14
Read Re: 4 colors problem
Virgil
3/5/14
Read Re: 4 colors problem
stumblin' in
3/6/14
Read Re: 4 colors problem
Virgil
3/6/14
Read Re: 4 colors problem
Virgil
3/6/14
Read Re: 4 colors problem
Brian Q. Hutchings
3/6/14
Read Re: 4 colors problem
stumblin' in
3/6/14
Read Re: 4 colors problem
ross.finlayson@gmail.com
3/7/14
Read Re: 4 colors problem
Brian Q. Hutchings
3/7/14
Read Re: 4 colours problem
Robin Chapman
3/6/14
Read Re: 4 colors problem
stumblin' in
3/6/14
Read Re: 4 colors problem
stumblin' in
3/7/14
Read Re: 4 colors problem
magidin@math.berkeley.edu
3/7/14
Read Re: 4 colors problem
Peter Percival
3/7/14
Read Re: 4 colors problem
Peter Percival
3/6/14
Read Re: 4 colors problem
stumblin' in
3/7/14
Read Re: 4 colors problem
stumblin' in
3/7/14
Read Re: 4 colors problem
magidin@math.berkeley.edu
3/7/14
Read Re: 4 colors problem
Peter Percival
3/7/14
Read Re: 4 colors problem
Peter Percival
3/7/14
Read Re: 4 colors problem
stumblin' in
3/7/14
Read Re: 4 colors problem
stumblin' in
3/9/14
Read Re: 4 colors problem
stumblin' in
3/9/14
Read Re: 4 colors problem
Peter Percival
3/9/14
Read Re: 4 colors problem
stumblin' in
3/9/14
Read Re: 4 colors problem
magidin@math.berkeley.edu
3/9/14
Read Re: 4 colors problem
Brian Q. Hutchings
3/9/14
Read Re: 4 colors problem
stumblin' in
3/9/14
Read Re: 4 colors problem
stumblin' in
3/11/14
Read Re: 4 colors problem
stumblin' in
3/11/14
Read Re: 4 colors problem
Brian Q. Hutchings
3/13/14
Read Re: 4 colors problem
stumblin' in
3/13/14
Read Re: 4 colors problem
Brian Q. Hutchings
3/13/14
Read Re: 4 colors problem
stumblin' in

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