Traversing an icosahedron

Probability Level 3

A bug can move along one edge of an icosahedron every 10 seconds. How many ways are there for it to move from one vertex to the opposite vertex in 30 seconds?

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The answer is 10.

Geoff Pilling by Geoff Pilling , 53, USA

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2 solutions

Aditi Chauhan
Apr 20, 2016

There are 5 ways to select an initial path from an end vertex, then 2 ways after moving through one edge/ for 10 seconds, and only 1 way to reach the opposite vertex Therefore number of ways = 5.2.1 =10

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Geoff Pilling
Apr 18, 2016

There are 2 ways for it to get to each of the five vertices connected to the opposite vertex by an edge. Therefore, there are 10 ways for it to get to the opposite vertex all together

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