There are n dots which are on a plane (flat surface). There are two players, A and B, who move alternatively; A moves first. The rules of the game are the same for both players: at each move they can connect two points, but they cannot connect points which were already directly connected to each other or connect a point with itself.

To put it simply, they build a graph (with predefined n vertices) by connecting some of the dots. The winner is the one who makes the graph connected (a graph is connected if there is a path between any two nodes of the graph, however, not every two nodes have to be connected directly). What is the winning strategy for player A, if such exists

SOME OF HELPFUL HINTS

• Clearly, if n = 2, the first player always wins.

•If n = 3, the second player always wins.

•If n = 4, the first player has a winning strategy.

•What if n =14?

• I suggest you find yourselves a partner its way more fun (unless you like playing with yourself) and play several games where n = 14. Determine which player (first or second) has a winning strategy? Provide convincing argument.

•Try then the general case (more involving)