Paint the points on a plane with three colors, so that the points on each line are a maximum of 2 colors, and all three colors are used. (Math Festival 1990)


You can do this by painting as follows:

Paint the origin blue, the rest of the x-axis red, and everything else green.

Any horizontal line will be either all green, or red and blue. Any nonhorizontal line will be all green except where it intersects the x-axis, so it will only have two colors: green and something else.

(You could actually paint the x-axis in any combination of red and blue you wanted, as long as it used both of them.)

  • $\begingroup$ You beat me to it by a matter of seconds. I'll just add that any line at all can be used in lieu of the x axis. $\endgroup$ – msh210 Jan 6 at 13:18
  • $\begingroup$ You could also paint both x and y axes red (except the origin), or any number of lines going thru the center. $\endgroup$ – Florian F Jan 6 at 13:29
  • $\begingroup$ @Deusovi why a horizontal line could be blue?? $\endgroup$ – MathR Jan 6 at 13:39
  • $\begingroup$ @Reza It cannot be entirely blue. It can be both red and blue, if it's the line at y=0. $\endgroup$ – Deusovi Jan 6 at 13:41
  • $\begingroup$ @Deusovi Thanks $\endgroup$ – MathR Jan 6 at 13:42

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