2023 AMC 10 A

Complete problem set with solutions and individual problem pages

Problem 25 Easy

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, if \overline{AB} is an edge of the polyhedron, then d(A. B) = 1, but if \overline{AC} and \overline{CB} are edges and \overline{AB} is not an edge,then d(A. B) = 2. Let O, R, and S be randomly chosen distinct vertices of regular icosahedron (regular polyhedron made up of 20 equilateral triangles). What is the probability that d( Q , R ) > d ( R , S )?

  • A.

    \frac { 7 } { 2 2 }

  • B.

    \frac { 1 } { 3 }

  • C.

    \frac { 3 } { 8 }

  • D.

    \frac { 5 } { 1 2 }

  • E.

    \frac { 1 } { 2 }

Answer:C
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