The Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.


Math Forum » Discussions » Math Topics » geometry.research

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Danny Purvis

Posts: 176
Registered: 12/6/04
Game of Sprouts n=12
Posted: Jan 28, 1999 10:05 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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
survivors.

(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.





Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2017. All Rights Reserved.