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Understanding a proof on IMO shortlist 2016 C3
The problem goes as follow:
Let $n$ be a positive integer relatively prime to 6. We paint the vertices of a regular
$n$-gon with three colours so that there is an odd number of vertices of each colour....
- 800
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Consider the diagonals of a 21-gon. Prove that at least one angle of less than 1 degree is formed.
I think it should be solved using the pigeonhole principle. The answer is:
A $21-$gon has $189$ diagonals. If through a point in the plane, we draw parallels to these diagonals, $2 × 189 = 378$ ...
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