M - married N - not married
N - married L - not married 
L - not married - M - married

When M is married and L and N are not married. This does not violate any 
condition but you have only 1 of the 3 people married.
When N is married, by condition (2) L is not married which implies M is 
married (by 3) and this implies N is not married by (1). A contradiction.
When L is married, implies, N cannot be married (otherwise by (2) L has to 
be unmarried). This poses no difficulty to M being married.

Therefore, L is married to M.

--
DK

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