MEMO 2007 T3

A tetrahedron is called a MEMO-tetrahedron if all six sidelengths are different positive integers where one of them is $2$ and one of them is $3$ . Let $l(T)$ be the sum of the sidelengths of the tetrahedron $T$ . (a) Find all positive integers $n$ so that there exists a MEMO-Tetrahedron $T$ with $l(T)=n$ . (b) How many pairwise non-congruent MEMO-tetrahedrons $T$ satisfying $l(T)=2007$ exist? Two tetrahedrons are said to be non-congruent if one cannot be obtained from the other by a composition of reflections in planes, translations and rotations. (It is not neccessary to prove that the tetrahedrons are not degenerate, i.e. that they have a positive volume).