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Fires of planets of Phoenix

Posted: Tue Apr 06, 2021 10:37 am
by Enthurelxyz
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. :(]

Re: Fires of planets of Phoenix

Posted: Tue Apr 06, 2021 11:17 am
by Mehrab4226
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 $F$.