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Introduction Graph theory is a mathematical discipline that spans a level of complexity ranging from childrens games to manipulation at the hands of some of todays leading mathematicians It is taught at levels varying from rather simple to extremely complex and is a growing discipline Sprouts for Spring Of Sprouts for Spring author Ivars Peterson says The game of sprouts has a way of growing on you This two-person pencil-and-paper game is simple enough that children can play it Yet its intricacies provide much food for mathematical thought Players begin with dots scattered on a sheet of paper In turn players have a choice of either connecting two of the dots with a line or beginning at a dot and looping back to the same dot Whether the player chooses to draw a line or a loop he then places another dot somewhere on the line or loop he has just drawn Rules are that lines and loops may be of any shape but they may not cross themselves or a previously drawn line or loop They may not pass through a previously made dot and no dot may have more than three lines emanating from it This stipulation results in the new dot placed on each line or loop as it is drawn already having two connections and so is available for only one more The last one able to play is the winner The intricacies Peterson speaks of involve the mathematical analysis of the game enough of which has been done that players often can determine at the beginning which of them will win simply by knowing how many dots they are beginning with Bell Labs computing power under the direction of three investigators revealed that the first player will win games beginning with nine ten or eleven dots while the second will win games beginning with either seven or eight dots Even though it appears the game could
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