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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 ISSN 0002-9890.
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Official URL: http://dx.doi.org/10.4169/amer.math.monthly.121.03...
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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > 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: |
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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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