Question

public static class MyExtensions
{
    /// <summary>
    /// Finds the missing numbers in a list.
    /// </summary>
    /// <param name="list">List of numbers</param>
    /// <returns>Missing numbers</returns>
    public static IEnumerable<int> FindMissing(this List<int> list)
    {
        // Sorting the list
        list.Sort();

        // First number of the list
        var firstNumber = list.First();

        // Last number of the list
        var lastNumber = list.Last();

        // Range that contains all numbers in the interval
        // [ firstNumber, lastNumber ]
        var range = Enumerable.Range(firstNumber, lastNumber - firstNumber);

        // Getting the set difference
        var missingNumbers = range.Except(list);

        return missingNumbers;
    }
}

Now you can call the extension method in the following way:

class Program
{
    static void Main(string[] args)
    {
        // List of numbers
        List<int> daysOfMonth =
        new List<int>() { 6, 2, 4, 1, 9, 7, 3, 10, 15, 19, 11, 18, 13, 22, 24, 20, 27, 31, 25, 28 };

        Console.Write("\nList of days: ");

        foreach(var num in daysOfMonth)
        {
            Console.Write("{0} ", num);
        }

        Console.Write("\n\nMissing days are: ");

        // Calling the Extension Method in the List of type int 
        foreach(var number in daysOfMonth.FindMissing())
        {
            Console.Write("{0} ", number);
        }
    }
}

Answer 1

public static IEnumerable<int> FindMissing(List<int> list)
{
    if (list.Count < 3) yield break;
    List<int> listClone = new List<int>(list); //do not modify the original list
    listClone.Sort();
    for (int n = listClone[i] ; n < listClone[listClone.Count - 1]; n++)
        if (!listClone.Contains(n))
            yield return n;
}

And of course this may be optimized not to traverse the entire listClone every time