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:

- Write a C++ program that prints out its own source code (do not read the source file and print it).
- Find an explicit formula for the ordinary generating function
of the following recurrence relation:

a_{n}= a_{n-1}+ a_{n-2}+ a_{n-3}, a_{0}= 1, a_{1}= 1, a_{2}= 2. - The golden sequence is defined as follows:

S_{0}= "0"

S_{n}= In S_{n-1}replace every occurrence of "0" by "1" and every occurrence of "1" by "10"

Prove that S_{n}= S_{n-1}+ S_{n-2}for n ≥ 2 (here + means string concatenation).

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Free Software Foundation

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