Code breaking and 3Q

The code breaking in the file. Q1: in how many ways can a one select three integers from the set {1,2,3,...,100} such that their sum is divisible by 3? Q2: The distance between two vertices in the same component of a graph is the length of a shortest path joining these vertices. If G is a connected graph, then the diameter of G is the maximum of all of the distances between the vertices of G. Prove: if G1 and G2 are complementary graphs, then at least one of them must be connected. (Hint: show that if G1 is disconnected, then the diameter of G2 is at most 2). Q3: Either draw a graph or tree with the given specifications or explain why no such graph or tree exists: Simple graph, six vertices having degrees 1,2,3,4,5,5