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In 1976 Martin Gardner posed the following problem: ``What is the smallestnumber of [queens] you can put on an [$n \times n$ chessboard] such that no[queen] can be added without creating three in a row, a column, or adiagonal?'' The work of Cooper, Pikhurko, Schmitt and Warrington showed thatthis number is at least $n$, except in the case when $n$ is congruent to $3$modulo $4$, in which case one less may suffice. When $n>1$ is odd, Gardnerconjectured the lower bound to be $n+1$. We prove this conjecture in the casethat $n$ is congruent to 1 modulo 4. The proof relies heavily on a recentadvancement to the Combinatorial Nullstellensatz for zero-sum grids due toBogdan Nica.

Repeatedly applying the Combinatorial Nullstellensatz for Zero-sum Grids to Martin Gardner's minimum no-3-in-a-line problem