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 more elevated a culture, the richer its language. The number of words and their combinations depends directly on a sum of conceptions and ideas; without the latter there can be no understandings, no definitions, and, as a result, no reason to enrich a language.”
—Anton Pavlovich Chekhov (1860–1904)
“I wonder love can have already set
In dreams, when we’ve not met
More times than I can number on one hand.”
—Philip Larkin (1922–1986)
“And if I pray, the only prayer
That moves my lips for me
Is—‘Leave the heart that now I bear,
And give me liberty.’”
—Emily Brontë (1818–1848)