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Omni-MATH / Let P be a convex n polygon each of which sides and diagnoals is colored with one of n distinct colors. For which n does: there exists a coloring method such that for any three of …

Problem

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problem

Let

P

be a convex

n

polygon each of which sides and diagnoals is colored with one of

n

distinct colors. For which

n

does: there exists a coloring method such that for any three of

n

colors, we can always find one triangle whose vertices is of

P

' and whose sides is colored by the three colors respectively.

Plain-text mathematical notation (without MathML)

Let P be a convex n polygon each of which sides and diagnoals is colored with one of n distinct colors. For which n does: there exists a coloring method such that for any three of n colors, we can always find one triangle whose vertices is of P' and whose sides is colored by the three colors respectively.

Original LaTeX notation

Let $ P$ be a convex $ n$ polygon each of which sides and diagnoals is colored with one of $ n$ distinct colors. For which $ n$ does: there exists a coloring method such that for any three of $ n$ colors, we can always find one triangle whose vertices is of $ P$' and whose sides is colored by the three colors respectively.

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task_id: 4a142bcd-fa9e-5d6a-8be2-6ece1c2ad5ae
task_key: test--4a142bcd-fa9e-5d6a-8be2-6ece1c2ad5ae
task_revision_id: 3
config / split: / test

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