In this note we study, for 𝓃 = 5,6,7, the geometry of the full flag manifolds, F( 𝓃 ) = U( 𝓃 )/U(1)x ⋅⋅⋅ x U(1). By using tournaments we characterize all of the (1,2)-symplectic invariant metrics on F( 𝓃 ), for 𝓃 = 5,6,7, corresponding to different classes of non-integrable invariant almost complex structure.