HMMT 2006 U17
- Guts
- Answer
Begining at a vertex, an ant is crawls between the vertices of a regular octahedron. After reaching a vertex, it randomly picks a neighboring vertex (sharing an edge) and walks to that vertex along the adjoining edge (with all possibilities equally likely.) What is the probability that after walking along 2006 edges, the ant returns to the vertex where it began?
Dataset text NuminaMath olympiads. Quoted with source.
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\frac{2^{2005}+1}{3 \cdot 2^{2006}}
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