What is Graph Pebbling:
Graph pebbling is a game played on a graph by two players. Player 1 buys n very expensive pebbles and gives them to player 2. Then player 2 distributes the pebbles on the vertices of the graph and chooses a target vertex t. Player 1 then plays a sequence of moves. If player 1 can place a pebble on t then he wins, otherwise player 2 wins. A move consists of removing two pebbles from one vertex and adding one pebble to a neighboring vertex. The pebbling number of a graph G, denoted π(G), is the smallest number of pebbles player 1 must buy in order to guarantee victory.

Some fun exercises:
1. Write a C++ program that prints out its own source code (do not read the source file and print it).
2. Find an explicit formula for the ordinary generating function of the following recurrence relation:
an = an-1 + an-2 + an-3, a0 = 1, a1 = 1, a2 = 2.
3. The golden sequence is defined as follows:
S0 = "0"
Sn = In Sn-1 replace every occurrence of "0" by "1" and every occurrence of "1" by "10"
Prove that Sn = Sn-1 + Sn-2 for n ≥ 2 (here + means string concatenation).