On Wednesday, October 2, 2013 12:17:25 PM UTC-4, 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.