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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.
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Notes on contributors
Alec S. Cooper
ALEC S. COOPER is currently an undergraduate at Middlebury College, planning to obtain his B.A. in mathematics in May 2013. He is particularly interested in algebra and other areas of discrete mathematics.
Oleg Pikhurko
OLEG PIKHURKO received his Ph.D. in mathematics from Cambridge University in 2000. He has an Erdős number of two and an Erdős Lap number of two. Although he is the founder and CEO of the Hedgehog Fund, it is unclear if he will have a finite Hedgehog Lap number.
John R. Schmitt
JOHN R. SCHMITT received his B.A. from Providence College in 1994, his M.S. from the University of Vermont in 1998, and his Ph.D. from Emory University in 2005. He currently teaches at Middlebury College, where he devotes his research time to extremal combinatorics and graph theory. He enjoys time spent with his wife and four children.
Gregory S. Warrington
GREGORY S. WARRINGTON, an algebraic combinatorialist at the University of Vermont, received his Ph.D. in mathematics from Harvard University in 2001. He likes to spend time with his family.