## Fires of planets of Phoenix

For discussing Olympiad Level Combinatorics problems
Enthurelxyz
Posts: 17
Joined: Sat Dec 05, 2020 10:45 pm
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### Fires of planets of Phoenix

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
Posts: 212
Joined: Sat Jan 11, 2020 1:38 pm

### Re: Fires of planets of Phoenix

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