Hogwarts Mystery 2020

It’s time for the Celestial Ball at Hogwarts. But due to the ongoing pandemic this year, the Ministry of Magic has decided to arrange the Ball to a limited extent. At most $k$ couples will be able to stay and dance in the Great Hall at a time maintaining social distancing. The Ball will continue for $n$ hours and exactly $n$ couples have registered for the Ball.

This is a companion discussion topic for the original entry at https://toph.co/p/hogwarts-mystery-2020