Sprouts (game) - Number of Moves

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 believe if we introduced the Lord’s Prayer here, senators would propose a large number of amendments to it.
    Henry Wilson (1812–1875)

    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)

    If anyone should want to know my name, I am called Leah. And I spend all my time weaving garlands of flowers with my fair hands, to please me when I stand before the mirror; my sister Rachel sits all the day long before her own, and never moves away. She loves to contemplate her lovely eyes; I love to use my hands to adorn myself: her joy is in reflection, mine in act.
    Dante Alighieri (1265–1321)