MEMO 2007 ekipno problem 7

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Dodao/la: arhiva
28. travnja 2012.
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).
Izvor: Srednjoeuropska matematička olimpijada 2007, ekipno natjecanje, problem 7