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$N$ lines are drawn in a plane. Proof that we can paint all the sectors in $2$ different colors, so any two neighbors (border's length is $>0$ (not just a point) ) are in different colors?

I am really stuck with this one. Any tips? Thank you :)

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That's a classical combinatorial geometry problem with a very nice solution: we do it by induction on the number of lines.

When there's 1 line, it's easy.

Next, suppose we've succeeded for $n$ lines. Then add more line and invert all colors on one side of it :) You can fill in the details.

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  • $\begingroup$ Cloud you please tell me the name of the problem or tell me where i can read more about it ? Thank you :) $\endgroup$ – Simon Jachson Apr 15 '17 at 21:46

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