Difference between revisions of "1993 AIME Problems/Problem 10"
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== Problem == | == Problem == | ||
+ | Euler's formula states that for a convex polyhedron with <math>V\,</math> vertices, <math>E\,</math> edges, and <math>F\,</math> faces, <math>V-E+F=2\,</math>. A particular convex polyhedron has 32 faces, each of which is either a triangle or a pentagon. At each of its <math>V\,</math> vertices, <math>T\,</math> triangular faces and <math>P^{}_{}</math> pentagonal faces meet. What is the value of <math>100P+10+V\,</math>? | ||
== Solution == | == Solution == | ||
+ | {{solution}} | ||
== See also == | == See also == | ||
− | + | {{AIME box|year=1993|num-b=9|num-a=11}} |
Revision as of 23:18, 25 March 2007
Problem
Euler's formula states that for a convex polyhedron with vertices, edges, and faces, . A particular convex polyhedron has 32 faces, each of which is either a triangle or a pentagon. At each of its vertices, triangular faces and pentagonal faces meet. What is the value of ?
Solution
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See also
1993 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |