1. How many edges does a complete graph with 11 vertices have?

2. Draw a tournament with five vertices which has five cyclic triples.  What is the score sequence of this tournament?

Think about, but don't hand in:  Can the directions of some of the edges of the tournament in the previous problem be changed so as to give a tournament with more than five cyclic triples?  Can the directions be changed to produce a tournament with exactly four cyclic triples?

3. For each of these three sequences

  (a)   (1, 1, 2, 2)                  (b)   (0, 2, 2, 2)                 (c)   (1, 1, 2, 3)

either draw a tournament having the sequence as a score sequence, or explain why there is no such tournament,