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On a combinatorial game with an application to Go-moku

✍ Scribed by L. Csmiraz

Publisher
Elsevier Science
Year
1980
Tongue
English
Weight
480 KB
Volume
29
Category
Article
ISSN
0012-365X

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✦ Synopsis

Let A be a finite set and 9 be a family of its subsets. Two players pick m resp. n points alternately from A. I wins if he picks all the points of some element of 9, otherwise II wins. We give a sufficient condition for II to have a winning strategy. Using this we prove the following statement. If in Go-moku I occupies m places, and II occupies n places in each turn, then, in case of m > n, I may have an arbitrarily long row of his places; in case m G n, II may bound the length of the rows occupied I.

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