Fires of planets of Phoenix

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Enthurelxyz
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Fires of planets of Phoenix

Unread post by Enthurelxyz » Tue Apr 06, 2021 10:37 am

In phoenix, a Galaxy far, far away, there are $2021$ planets. Define a $fire$ to be a path between two objects
in phoenix. It is known that between every pair of planets either a single fire burns or no burning occurs.
If we consider any subset of $2019$ planets, the total number of fires burning between these planets is a
constant. If there are $F$ fires in phoenix, then find all possible values of $F$.

I have not understood the problem. Please help me to understand it. [Note: I am not good at English. :(]
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Mehrab4226
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Re: Fires of planets of Phoenix

Unread post by Mehrab4226 » Tue Apr 06, 2021 11:17 am

Enthurelxyz wrote:
Tue Apr 06, 2021 10:37 am
In phoenix, a Galaxy far, far away, there are $2021$ planets. Define a $fire$ to be a path between two objects
in phoenix. It is known that between every pair of planets either a single fire burns or no burning occurs.
If we consider any subset of $2019$ planets, the total number of fires burning between these planets is a
constant. If there are $F$ fires in phoenix, then find all possible values of $F$.

I have not understood the problem. Please help me to understand it. [Note: I am not good at English. :(]
Let there are $2021$ points in a plane. $2$ points can be either connected by a line or not. If you choose any $2019$ points and count the number of lines present in the $2019$ points then the number of lines will always be constant. If $F$ is the total number of lines in the plane. Find all the possible values of $F$.
The Mathematician does not study math because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.
-Henri Poincaré

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