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Martin Gardner’s minimum No-3-in-a-line problem

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Cooper, Alec S., Pikhurko, Oleg, Schmitt, John R. and Warrington, Gregory S. (2014) Martin Gardner’s minimum No-3-in-a-line problem. The American Mathematical Monthly, 121 (3). pp. 213-221. doi:10.4169/amer.math.monthly.121.03.213

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Official URL: http://dx.doi.org/10.4169/amer.math.monthly.121.03...

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Abstract

In Martin Gardner’s October 1976 Mathematical Games column in Scientific American, he posed the following problem: “What is the smallest number of [queens] you can put on an [n × n chessboard] such that no [queen] can be added without creating three in a row, a column, or, except in the case when n is congruent to 3 modulo 4, in which case one less may suffice.” We use the Combinatorial Nullstellensatz to prove that this number is at least n. A second, more elementary proof is also offered in the case that n is even.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Puzzles
Journal or Publication Title: The American Mathematical Monthly
Publisher: Mathematical Association of America
ISSN: 0002-9890
Official Date: March 2014
Dates:
DateEvent
March 2014Published
Volume: 121
Number: 3
Number of Pages: 9
Page Range: pp. 213-221
DOI: 10.4169/amer.math.monthly.121.03.213
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Funder: National Science Foundation (U.S.) (NSF), United States. National Security Agency (USNSA), Simons Foundation (SF)
Grant number: DMS-1100215 (NSF), DMS-0758057 (NSF), H98230-10-1-0173 (USNSA), H98230-09-1-0023 (USNSA), 197419 (SF)

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