# Traveling Through Triangles

Brilli the ant stands on node 1 of the figure below.

Every minute, Brilli picks an adjacent node at random and moves to it. Each adjacent node has the same chance to be picked. For example, when Brilli is on node 2, he could move to nodes 1, 3, 4, or 5, each with a $$\frac{1}{4}$$ probability.

What is the expected value of the number of moves Brilli will need to make to get to node 5?

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