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:
“He is the richest man who knows how to draw a benefit from the labors of the greatest number of men, of men in distant countries, and in past times.”
—Ralph Waldo Emerson (1803–1882)
“After a certain number of years our faces become our biographies. We get to be responsible for our faces.”
—Cynthia Ozick (b. 1928)
“You like it under the trees in autumn,
Because everything is half dead.
The wind moves like a cripple among the leaves
And repeats words without meaning.”
—Wallace Stevens (1879–1955)