Shortest string containing all fixed-length substrings
This is called a de Bruijn sequence ( http://en.wikipedia.org/wiki/De_Bruijn_sequence ).  You can generate it by taking an Euler tour of a de Bruijn graph, but there are also other ways.  You can use de Bruijn sequences to break into 1990s-era cars efficiently ( http://everything2.com/title/Weak+security+in+our+daily+lives ) among many other applications.