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:
“I who have been involved with all styles of painting can assure you that the only things that fluctuate are the waves of fashion which carry the snobs and speculators; the number of true connoisseurs remains more or less the same.”
—Pablo Picasso (1881–1973)
“The best number for a dinner party is two—myself and a dam’ good head waiter.”
—Nubar Gulbenkian (1896–1972)
“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)