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arXiv · 2609.05780

An infinite walk in $\mathbb{N}^{16}$, using only unit steps, with no three collinear points

Jeffrey Shallit
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Abstract

Is it possible to walk to infinity, avoiding three collinear points, using as steps only the standard unit basis vectors $(0,0,\ldots, 0, 1, 0, \ldots, 0)$? We prove this is possible in $16$ dimensions.

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Jeffrey Shallit. 2026-09-05. An infinite walk in $\mathbb{N}^{16}$, using only unit steps, with no three collinear points. https://arxiv.org/abs/2609.05780

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