Difference between revisions of "2023 AMC 10A Problems/Problem 25"
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| + | If A and B are vertices of a polyhedron, define the distance d(A, B) to be the minimum number of edges of the polyhedron one must traverse in order to connect A and B. For example, <math>\overline{AB}</math> is an edge of the polyhedron, then d(A, B) = 1, but if <math>\overline{AC}</math> and <math>\overline{CB}</math> are edges and <math>\overline{AB}</math> is not an edge, then d(A, B) = 2. Let Q, R, and S be randomly chosen distinct vertices of a regular icosahedron (regular polyhedron made up of 20 equilateral triangles). What is the probability that <math>d(Q, R) > d(R, S)</math>? | ||
| + | <math>\textbf{(A) }\frac{7}{22}\qquad\textbf{(B) }\frac{1}{3}\qquad\textbf{(C) }\frac{3}{8}\qquad\textbf{(D) }\frac{5}{12}\qquad\textbf{(E) }\frac{1}{2}</math> | ||
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| + | == Video Solution 1 by OmegaLearn == | ||
| + | https://youtu.be/Wc6PFNq5PAM | ||
Revision as of 16:16, 9 November 2023
If A and B are vertices of a polyhedron, define the distance d(A, B) to be the minimum number of edges of the polyhedron one must traverse in order to connect A and B. For example, 
is an edge of the polyhedron, then d(A, B) = 1, but if 
and 
are edges and is not an edge, then d(A, B) = 2. Let Q, R, and S be randomly chosen distinct vertices of a regular icosahedron (regular polyhedron made up of 20 equilateral triangles). What is the probability that 
?
