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:
“To finish the moment, to find the journey’s end in every step of the road, to live the greatest number of good hours, is wisdom. It is not the part of men, but of fanatics, or of mathematicians, if you will, to say, that, the shortness of life considered, it is not worth caring whether for so short a duration we were sprawling in want, or sitting high. Since our office is with moments, let us husband them.”
—Ralph Waldo Emerson (1803–1882)
“There is something tragic about the enormous number of young men there are in England at the present moment who start life with perfect profiles, and end by adopting some useful profession.”
—Oscar Wilde (1854–1900)
“Speech and prose are not the same thing. They have different wave-lengths, for speech moves at the speed of light, where prose moves at the speed of the alphabet, and must be consecutive and grammatical and word-perfect. Prose cannot gesticulate. Speech can sometimes do nothing more.”
—James Kenneth Stephens (1882–1950)