3.58 On the vertices of some congruent equilateral triangles, write the numbers $1, 2, 3$ in any order. Stack these triangles together so that their vertices coincide. Can the sum of the numbers at each vertex be (1) 1977? (2) 1976?
[Solution] Since the sum of the three numbers at the vertices of each triangle is 6, no matter how many triangles are stacked together, the sum of all integers at the three vertices will always be a multiple of 6. Since $3 \times$ 1977 is not a multiple of 6, it is impossible for the sum of the integers at each vertex of the stacked triangles to be 1977.

Note, if you simply overlap two equilateral triangles so that the vertex with 1 in one triangle coincides with the vertex with 3 in the other triangle, the vertex with 3 in one triangle coincides with the vertex with 1 in the other triangle, and the vertices with 2 in both triangles also coincide, then the sum of the two numbers at each vertex will be 4. Since $1976=4 \times 494$, by stacking 494 pairs of triangles that have been overlapped in the manner described above, the sum of the numbers at each vertex of the resulting stacked triangle will be 1976.