There are 2020 people in a room. One person has a COVID.

After each minute, each person $\mathrm{P}$ is paired with some other person $\mathrm{Q}$ who was never paired with $\mathrm{P}$ before, and coughs to each other. If one of $\mathrm{P}$ and $\mathrm{Q}$ has COVID and other does not, the other gets COVID. If both do not have COVID or both have COVID, nothing happens.

If you can choose the people in each pair for every minute and you'd like to delay everyone getting infected, how long would it take for everyone in the room to get COVID?

(The answer seems to depend a lot on the number of people N=2020, and I have a strategy to get m^2-2m+1 minutes if N=m^2, I am not sure if this is optimal)

[[Questions like this in a random pairing setting are well studied in graph theory/information broadcasting; This question is about the upper bounds and the worst case for the information/infection to spread. But this specific formulation is not mine, someone recently asked me this question, I don't have the source, But it's probably from some Facebook group “actually good math problems” which I don't have access to.]]

There are 2020 people in a room. One person has COVID.

After each minute, each person $\mathrm{P}$ is paired with some other person $\mathrm{Q}$ who was never paired with $\mathrm{P}$ before, and they cough to each other. If one of $\mathrm{P}$ and $\mathrm{Q}$ has COVID and other does not, the other gets COVID. If both do not have COVID or both have COVID, nothing happens.

If you can choose the people in each pair for every minute and you'd like to delay everyone getting infected for as long as possible, then how long would it take for everyone in the room to get COVID?

(The answer seems to depend a lot on the number of people N=2020, and I have a strategy to get m^2-2m+1 minutes if N=m^2, I am not sure if this is optimal)

[[Questions like this in a random pairing setting are well studied in graph theory/information broadcasting; This question is about the upper bounds and the worst case for the information/infection to spread. But this specific formulation is not mine, someone recently asked me this question, I don't have the source, But it's probably from some Facebook group “actually good math problems” which I don't have access to.]]

There are 2020 people in a room. One person has a COVID.

After each minute, each person $\mathrm{P}$ is paired with some other person $\mathrm{Q}$ who was never paired with $\mathrm{P}$ before, and coughs to each other. If one of $\mathrm{P}$ and $\mathrm{Q}$ has COVID and other does not, the other gets COVID. If both do not have COVID or both have COVID, nothing happens.

If you can choose the people in each pair for every minute and you'd like to delay everyone getting infected, how long would it take for everyone in the room to get COVID?

(The answer seems to depend a lot on the number of people N=2020, and I have a strategy to get m^2-2m+1 minutes if N=m^2, I am not sure if this is optimal)

There are 2020 people in a room. One person has a COVID.

After each minute, each person $\mathrm{P}$ is paired with some other person $\mathrm{Q}$ who was never paired with $\mathrm{P}$ before, and coughs to each other. If one of $\mathrm{P}$ and $\mathrm{Q}$ has COVID and other does not, the other gets COVID. If both do not have COVID or both have COVID, nothing happens.

If you can choose the people in each pair for every minute and you'd like to delay everyone getting infected, how long would it take for everyone in the room to get COVID?

(The answer seems to depend a lot on the number of people N=2020, and I have a strategy to get m^2-2m+1 minutes if N=m^2, I am not sure if this is optimal)

[[Questions like this in a random pairing setting are well studied in graph theory/information broadcasting; This question is about the upper bounds and the worst case for the information/infection to spread. But this specific formulation is not mine, someone recently asked me this question, I don't have the source, But it's probably from some Facebook group “actually good math problems” which I don't have access to.]]