
Re: cotpi 69  Black and white plane
Posted:
Oct 2, 2013 10:29 PM


"quasi" <quasi@null.set> wrote in message news:v9vo49lvr7j4ns7i82s869ou749lgdmrup@4ax.com... > Pubkeybreaker wrote: > >Susam Pal wrote: > >> > >> How can you construct a plane where every point is coloured > >> either black or white such that two points of the same colour > >> are never a unit distance apart? > >> > >>  Originally posted at: > >> http://cotpi.com/p/69/ > >> Puzzles IRC channel: > >> ##puzzles on irc.freenode.net > >> Puzzles IRC webchat: > >> http://webchat.freenode.net/?channels=##puzzles > > > >It does not seem possible. Take any point. Suppose it is > >white. It is the center of a circle (of radius 1). All points > >on that circle must then be black. But given any point on > >that circle there is another point on the circle at distance 1. > >Both points are the same color. > > > >Unless, of course, I am being completely stupid. > > No, your proof is fine. > > quasi
The question was asked here a few years ago whether the plane can be coloured along the lines above but using three colours. The answer is no, and the proof is similar but less obvious...
Regards, Mike.

