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)
“Ah, but to play man number one,
To drive the dagger in his heart,
To lay his brain upon the board
And pick the acrid colors out,
To nail his thought across the door,
Its wings spread wide to rain and snow,
To strike his living hi and ho....”
—Wallace Stevens (1879–1955)
“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)