37. Tetrahedron. There are 6 rods of different lengths, and it is known that in any order, a tetrahedron (triangular pyramid) can be formed from them. How many different tetrahedrons can result from this?
37. The answer depends on whether we consider two tetrahedra different if one can be obtained from the other by a mirror reflection. We will show that in the first case, there are 60 different tetrahedra; in the second case, the number will obviously be reduced to 30.

Consider Fig. 55, which shows a tetrahedron with edges labeled $a, b, c, d, e, f$. Let's number the rods from which we assembled the tetrahedron from 1 to 6; a rod can be used as any of the edges $a, b, c, d, e, f$. Therefore, we can form $6!=720$ tetrahedra, although some of them will differ only by their position in space.

Temporarily assume that the tetrahedron shown in Fig. 55 is regular. Let's determine how many ways this tetrahedron can be superimposed on itself by moving it in space. Clearly, the position of the tetrahedron is completely determined by $1^{\circ}$ which of the four faces of the tetrahedron is placed at the base and $2^{\circ}$ which of the three edges of this face is aligned with a fixed edge of the base, for example, with edge $a$. Therefore, there are a total of $3 \cdot 4 = 12$ different positions of the tetrahedron.

Thus, the 720 possible permutations of our rods, taken as edges $a-f$, form each tetrahedron 12 times, and therefore, there are $720: 12=60$ different tetrahedra that can be assembled from six different rods. If we identify tetrahedra that can be obtained from each other by a mirror reflection, then the number of different tetrahedra will be half as many, i.e., $60: 2=30$.