{"paper":{"title":"Minimal and maximal Numbrix puzzles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David A. Nash, Mary Grace Hanson","submitted_at":"2017-06-20T10:40:32Z","abstract_excerpt":"This paper explores special arrangements of clues in $m \\times n$ Numbrix puzzles. The maximum number of clues which fails to define an $m \\times n$ puzzle is demonstrated for all $m$ and $n$. In addition, a small upper bound on the minimum number of clues required to define an $m \\times n$ puzzle is given for all $m$ and $n$ as well. For small $m \\geq 3$ our upper bound appears to actually give the minimum number and hence we conjecture that our bound may be sharp for all $m \\geq 3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09389","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}