Maths Puzzle :: Discussion

An ant is placed at one corner of a wire frame in the shape of a cube. At the diagonally opposite corner is a piece of sugar.The ant crawls along the all the wires of the frame searching for the sugar. At each of the 8 corners the ant randomly chooses one of the 3 wires to follow next (including the one it just traveled) What is the expected number of edges the Ant will traverse until it reaches the sugar?



What if the Ant never doubles back on the wire it just crossed?