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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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:	Date Event March 2014 Published
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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