Write a class with some properties and indexed
The inheritance doesn't make sense. 'PlacementLocations' is the object representing a collection of 'PlacementLocation' objects.

public class PlacementLocations
{
    private List&lt;PlacementLocation&gt; _placementLocations;

    public PlacementLocations(List&lt;PlacementLocation&gt; locations)
    {
        _placementLocations = locations;
    }

    public Tuple&lt;int, int&gt; this[int location]
    {
        get { return new Tuple&lt;int, int&gt;(_placementLocations[location].Row, _placementLocations[location].Column); }
    }

    public int this[int row, int column]
    {
        get
        {
            PlacementLocation singleOrDefault =
                _placementLocations.SingleOrDefault(d =&gt; d.Column == column &amp;&amp; d.Row == row);
            return singleOrDefault != null ? singleOrDefault.Location : 0;
        }
    }
}


Class should not contain particular initialization values: use constructor parameters instead and initialize externally:

...

var placementLocationList = new List&lt;PlacementLocation&gt;
{
    new PlacementLocation { Column = 1, Row = 9, Location = 1 },
    new PlacementLocation { Column = 2, Row = 9, Location = 2 },
    new PlacementLocation { Column = 3, Row = 9, Location = 3 },
    new PlacementLocation { Column = 4, Row = 9, Location = 4 },
    new PlacementLocation { Column = 5, Row = 9, Location = 5 },
};

var placementLocations = new PlacementLocations(placementLocationList);

...


Update:
if you need predefined locations list you can use some sort of factory...

public class LocationsFactory
{
    public static PlacementLocations GetPredefinedLocations()
    {
        var placementLocationList = new List&lt;PlacementLocation&gt;
        {
            new PlacementLocation { Column = 1, Row = 9, Location = 1 },
            new PlacementLocation { Column = 2, Row = 9, Location = 2 },
            new PlacementLocation { Column = 3, Row = 9, Location = 3 },
            new PlacementLocation { Column = 4, Row = 9, Location = 4 },
            new PlacementLocation { Column = 5, Row = 9, Location = 5 },
        };

        return new PlacementLocations(placementLocationList);
    }
}