Problem of the Week

Five people are standing around a field throwing a Frisbee back and forth.  When one of them catches the Frisbee, they throw it at random to one of the other players.  What is the largest sequence of consecutive throws in which no two players throw the Frisbee to each other twice? 

For instance, if there were only four people people playing, named Alfredo, Bernd, Cecile and Dagwood, then one such sequence of length ten might be ABCDADCBACA (note that no consecutive pair of letters is repeated, but the addition of any new letter would cause a repetition of either AB, AC or AD), though there is a longer sequence of length twelve

What is the longest sequence if an additional five people join the players, making it ten players in all?   

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ã2004 Alberto L. Delgado