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 basis of successful relief in national distress is to mobilize and organize the infinite number of agencies of self help in the community. That has been the American way.”
—Herbert Hoover (1874–1964)
“But however the forms of family life have changed and the number expanded, the role of the family has remained constant and it continues to be the major institution through which children pass en route to adulthood.”
—Bernice Weissbourd (20th century)
“I live in my wooden legs and O
my green green hands.
Too late
to wish I had not run from youpollo,
blood moves still in my bark bound veins.”
—Anne Sexton (1928–1974)