Euler's formula states that for a convex polyhedron with $$V\,$$ vertices, $$E\,$$ edges, and $$F\,$$ faces, $$V-E+F=2\,$$. A particular convex polyhedron has 32 faces, each of which is either a triangle or a pentagon. At each of its $$V\,$$ vertices, $$T\,$$ triangular faces and $$P^{}_{}$$ pentagonal faces meet. What is the value of $$100P+10T+V\,$$?

(第十一届AIME1993 第10题)