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Omni-MATH / We colour all the sides and diagonals of a regular polygon P with 43 vertices either red or blue in such a way that every vertex is an endpoint of 20 red segments and 22 blue segme…

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problem

We colour all the sides and diagonals of a regular polygon PP with 4343 vertices either red or blue in such a way that every vertex is an endpoint of 2020 red segments and 2222 blue segments. A triangle formed by vertices of PP is called monochromatic if all of its sides have the same colour. Suppose that there are 20222022 blue monochromatic triangles. How many red monochromatic triangles are there?
Plain-text mathematical notation (without MathML)
We colour all the sides and diagonals of a regular polygon P with 43 vertices either
red or blue in such a way that every vertex is an endpoint of 20 red segments and 22 blue segments.
A triangle formed by vertices of P is called monochromatic if all of its sides have the same colour.
Suppose that there are 2022 blue monochromatic triangles. How many red monochromatic triangles
are there?
Original LaTeX notation
We colour all the sides and diagonals of a regular polygon $P$ with $43$ vertices either
red or blue in such a way that every vertex is an endpoint of $20$ red segments and $22$ blue segments.
A triangle formed by vertices of $P$ is called monochromatic if all of its sides have the same colour.
Suppose that there are $2022$ blue monochromatic triangles. How many red monochromatic triangles
are there?

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Source and history

task_id
011a9010-710d-527e-baab-25e9c13b7799
task_key
test--011a9010-710d-527e-baab-25e9c13b7799
task_revision_id
1
config / split
/ test

Official source

initial import