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Topic: Game of Sprouts n=12
Replies: 2   Last Post: Apr 18, 1999 10:07 AM

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Danny Purvis

Posts: 176
Registered: 12/6/04
Game of Sprouts n=12
Posted: Jan 28, 1999 10:05 AM
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According to Ivars Peterson's 4/7/97 MathLand column, "A few years
ago, David Applegate, Guy Jacobson, and Daniel Sleator, then at Bell
Labs, used a lot of computer power to push the analysis of sprouts out
to eleven dots." The article goes on to discuss a prediction by the
three researchers concerning the twelve dot game. One gets the
impression that twelve dots must be very complicated, but actually
that is not the case. The second player wins by forcing eight

(L1) 12+ 1(13)1 1(14)13[2&3&4&5] (S<2>=3. S<2> is an N. X will
have to move first to S<6>. He might as well do that now.)
(L1a) 6(15)14 6(16)6[7&8&15] (S<7>=2.)
(L1b) 6(15)6 6(16)15[7&8&14] (S<7>=2. (Y has TM.))
(L1c) 6(15)6[7] 6(16)15[8&14] (S<7>=1. S<8>=1.)
(L1d) 6(15)6[7&8] 6(16)15[9&14] (S<10>=2. N+T.)
(L1e) 6(15)6[7&8&9] 6(16)15[10&11] (S<7>=2. N+T.)
(L1f) 6(15)6[7&8&14] 6(16)15[7] (S<9>=3.)
(L1g) 6(15)6[7&14] 6(16)15[8&9] (N+T.)
(L1h) 6(15)6[14] 6(16)15[7&8] (N+T.)
(L1i) 6(15)7 6(16)6[8&9&14] (S<7>=3. Y has TM. 10(17)11 10(18)11.)

(L2) 12+ 1(13)1[2] 1(14)13[3&4&5&6] (S<7>=4.)

(L3) 12+ 1(13)1[2&3] 1(14)13[4&5&6] (N+T.)

(L4) 12+ 1(13)1[2&3&4] 1(14)13[5&6&7&8]

(L5) 12+ 1(13)1[2&3&4&5] 1(14)13[6&7&8]

(L6) 12+ 1(13)1[2&3&4&5&6] 1(14)13[2&3] (N+T.)

(L7) 12+ 1(13)2 1(14)1[2&3&4&5] (S<2>=3. S<2> is an N. X will
have to move first to S<6>. See L1.

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