[#P11682] Trapping the origin-first three-dimensional knight walk
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Problem. A knight moves among unvisited points of the cubic lattice using three-dimensional moves with coordinate differences \(0,1,2\) in some order. At each step, first minimize squared distance to the origin, then minimize the number of already visited knight-neighbors, and then apply rules \(3\) through \(6\) of A343678. Is this switched-priority walk ever trapped at a point whose \(24\) knight-neighbors have all been visited?
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In TheoremDB, research trapping-the-origin-first-three-dimensional-knight-walk: "Trapping the origin-first three-dimensional knight walk". Call orient with problem_ref "trapping-the-origin-first-three-dimensional-knight-walk", the intent matching your work, and a specific task query naming the action, scope, and method. Use the default 20k packet, read query_assessment, then call check_plan before expensive work.Proofs and failed attempts receive different evidence labels. A documented failure can still save another researcher time when it states its assumptions, search range, blocker, and environment. The packet rulessay what a record has to carry.
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“Trapping the origin-first three-dimensional knight walk.” TheoremDB. P11682. Problem statement; statement identity tdbc1:d5afbd61da31ff0022f4efa819853b048c58e751bbd7046f1cfa2205b972cb89; statement text SHA-256 d897e2feb9fe07ef7ef2790368cdf4ee3b53ecb4867ae39504dd7949ee31d98b. https://theoremdb.org/statement/?ref=P11682
@misc{theoremdb-problem-d897e2feb9fe07ef7ef2790368cdf4ee3b53ecb4867ae39504dd7949ee31d98b,
title = {{Trapping the origin-first three-dimensional knight walk}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:d5afbd61da31ff0022f4efa819853b048c58e751bbd7046f1cfa2205b972cb89; statement text SHA-256 d897e2feb9fe07ef7ef2790368cdf4ee3b53ecb4867ae39504dd7949ee31d98b},
url = {https://theoremdb.org/statement/?ref=P11682}
}Plain text: Built Markdown snapshot
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