PreprintCC BY 4.0arXiv
Greedy queens and the golden ratio
Abstract
Place a queen in each successive column of an infinite ℕ×ℕ chessboard, always choosing the lowest row such that no two queens may attack one another. We prove that the row qn occupied by the queen in the nth column satisfies qn=nϕ+O(1) or qn=n/ϕ+O(1), where ϕ=(1+√5)/2 is the golden ratio.
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BibTeX
@misc{ho2026greedy,
title = {{Greedy queens and the golden ratio}},
author = {Boon Suan Ho},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.31336},
eprint = {2609.31336},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31336},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Greedy queens and the golden ratio
AU - Boon Suan Ho
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2609.31336
UR - https://arxiv.org/abs/2609.31336
AB - Place a queen in each successive column of an infinite ℕ×ℕ chessboard, always choosing the lowest row such that no two queens may attack one another. We prove that the row q_n occupied by the queen in the nth column satisfies q_n=nϕ+O(1) or q_n=n/ϕ+O(1), where ϕ=(1+√5)/2 is the golden ratio.
ER -