{"paper":{"title":"Complexity of 2D Snake Cube Puzzles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.CC","authors_text":"Alex Dang, Erik D. Demaine, Kaylee Ji, MIT Hardness Group, Nithid Anchaleenukoon, Pitchayut Saengrungkongka","submitted_at":"2024-07-14T20:31:03Z","abstract_excerpt":"Given a chain of $HW$ cubes where each cube is marked \"turn $90^\\circ$\" or \"go straight\", when can it fold into a $1 \\times H \\times W$ rectangular box? We prove several variants of this (still) open problem NP-hard: (1) allowing some cubes to be wildcard (can turn or go straight); (2) allowing a larger box with empty spaces (simplifying a proof from CCCG 2022); (3) growing the box (and the number of cubes) to $2 \\times H \\times W$ (improving a prior 3D result from height $8$ to $2$); (4) with hexagonal prisms rather than cubes, each specified as going straight, turning $60^\\circ$, or turning "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.10323","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.10323/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}