Using LINQ to join two string lists without repeats

I have a list of members that have to play a game against each other and I want to generate a complete list of all the members against every other member without repeating any games. My list looks like this:

string[] members = {"Alphie", "Jerome", "Silky", "Buzz" };

My first attempt at generating a list using LINQ was this:

IEnumerable<string> q = from one in members
                        from two in members
                        select one + " plays " + two;

which resulted in:

Alphie plays Alphie
Alphie plays Jerome
Alphie plays Silky
Alphie plays Buzz
Jerome plays Alphie
Jerome plays Jerome
Jerome plays Silky
Jerome plays Buzz
Silky plays Alphie
Silky plays Jerome
Silky plays Silky
Silky plays Buzz
Buzz plays Alphie
Buzz plays Jerome
Buzz plays Silky
Buzz plays Buzz

This is not exactly what I was looking for. I wonder who the winner would have been in Buzz versus Buzz?

The secret is to put a where clause before the select statement:

where one.CompareTo(two) < 0

This will eliminate duplicates when CompareTo(two) == 0 and also alphabetically sort the two players eliminating them playing against each other a second time. This is the complete code snippet:

IEnumerable<string> q = from one in members
                        from two in members
                        where one.CompareTo(two) < 0
                        select one + " plays " + two;

and here are the revised results:

Alphie plays Jerome
Alphie plays Silky
Alphie plays Buzz
Jerome plays Silky
Buzz plays Jerome
Buzz plays Silky