A generalization of Kaplansky's game

✍ Scribed by D.J. Kleitman; B.L. Rothschild

• Publisher: Elsevier Science
• Year: 1972
• Tongue: English
• Weight: 808 KB
• Volume: 2
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(72)90082-9

✦ Synopsis

kq&msky invented the fukwing game plrrysd on the ifiteger lattice point.5 (i. 1) of the plane. Two pIapzrs sltersu&4y choose distinct points. If there ever occurs during the play a configuration where some strGght M%~iteI line in the plane contains k points selected by one player and no points ;mywherq on it selected hy the other player, tflen the fomler plnyer wins. For instance, if k = \ ,_ the game is wan after the first plavcr makes ane choice. If A: = 2, the first plaver can always win on his se& and choice. It is easy to see ;also that doi k = 3 the first player can always win after making at must ftxer ch(dk%.

We catI this game the restriutcd game, and we consider ;1 vxiant of it, the urrrest'ricted gttme. The uniestrictcd g%me has the same rules except that the players anay snake their choices from all the points af the pfane instead afjust from the lattice points. The only relevant feature of the * I%is work was wppottad in part by NW Gratrts =I;P-23482 and P 22928. ** Rev&d mmian nrccivcd I8 Nwember 187 1.