Problem of the Week

An ant is standing at one of the corners of a regular tetrahedron.  Once each minute, the ant selects one of the adjacent corners at random and moves there.  What is the exact probability (no decimal approximations, please) that the ant is back where it started one week after it starts its walk? 

(A tetrahedron is a figure made up of  four vertices and four face each in the shape of an equilateral triangles.  Three of these faces come together at each of the four vertices.)

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ã2003 Alberto L. Delgado