1
$\begingroup$

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)

$\endgroup$
3
$\begingroup$

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.)

$\endgroup$
5
  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.