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.