Number of Moves
It is not evident from the rules of Sprouts that the game always terminates, since the number of spots increase at each move. The correct approach is to consider the number of lives (opportunities to connect a line) instead of the number of spots. Then, we can show that if the game starts with n spots, it will end in no more than 3n−1 moves and no fewer than 2n moves.
In the following proofs, we suppose that a game starts with n spots and lasts for exactly m moves.
Read more about this topic: Sprouts (game)
Famous quotes containing the words number of, number and/or moves:
“The two great points of difference between a democracy and a republic are: first, the delegation of the government, in the latter, to a small number of citizens elected by the rest; secondly, the greater number of citizens and greater sphere of country over which the latter may be extended.”
—James Madison (1751–1836)
“You are the majority—in number and intelligence; therefore you are the force—which is justice. Some are scholars, others are owners; a glorious day will come when the scholars will be owners and the owners scholars. Then your power will be complete, and no man will protest against it.”
—Charles Baudelaire (1821–1867)
“Think of the wonderful circles in which our whole being moves and from which we cannot escape no matter how we try. The circler circles in these circles....”
—E.T.A.W. (Ernst Theodor Amadeus Wilhelm)