A finite goal set in the plane which is not a Winner
Abstract
J. Beck has shown that if two players alternately select previously unchosen points from the plane, Player 1 can always build a congruent copy of any given finite goal set G, in spite of Player 2's efforts to stop him. We give a finite goal set G (it has 5 points) which Player 1 cannot construct before Player 2 in this achievement game played in the plane.
 Publication:

arXiv eprints
 Pub Date:
 January 2011
 arXiv:
 arXiv:1101.4420
 Bibcode:
 2011arXiv1101.4420P
 Keywords:

 Mathematics  Combinatorics;
 Computer Science  Computer Science and Game Theory
 EPrint:
 8 pages, 4 figures