Help with a C# assignment (Unique identifier)

I am having problems with an assignment of mine .I was instructed create a dummy grid world for a Party app (2D point array with coordinates for X,Y). From my understanding each coordinate has to have a maximum of 1 party assigned to them which has to be unique. At the moment, i am having a problem with my logic as i have passed a method to generate Parties which will return a list of Parties but i feel my logic as it flawed (see below). My plan is to return the results to the Cordinate class and loop over them so each cordinate has a random party id assigned to it

I already have a Coordinate Class which produces a Constructor Coordinate(x,y). this is fed into a Party World Class which constructs a 2D array for my World Grid

At the moment for my Party class i have

public class Party { static Random unique = new Random(); public List<int> Party { get; set; }

    public Party(int _count)
    {
        Party = Generate_EventId(_count);

    }

   public List<int> Generate_EventId(int count)
    {
        HashSet<int> partygen = new HashSet<int>();
        while (partygen.Count < count)
        {
            partygen.Add(unique.Next());
        }

       List<int> result = new List<int>();
        result.AddRange(partygen);
        return result;

    }

}

} The Assignment question specifically says; *Each party has a unique numeric identifier (e.g. 1, 2, 3) and should assume that each co-ordinate can hold a maximum of one event * [hence me using HashSet and Random]. However, i think i should be using a dictionary to generate the numbers using keys. Can someone help me with this please