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November 8, 2011

Ant on a Cube

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?

November 4, 2011

How many people are there?

How many people must be there if all but 2 are named Smith, all but 2 are named Jones, and all but 2 are named Wilson?