{"paper":{"title":"Automorphisms of $S_6$ and the Colored Cubes Puzzle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniel Condon, David Cervantes Nava, Ethan Berkove, Rachel Katz","submitted_at":"2015-03-24T20:17:32Z","abstract_excerpt":"Given a palette of six colors, a colored cube is a cube where each face is colored with exactly one color and each color appears on some face. Starting with an arbitrary collection of unit length colored cubes, one can try to arrange a subset of the collection into an $n \\times n \\times n$ cube where each face is a single color. This is the Colored Cubes Puzzle. In this paper, we determine minimum size sets of cubes required to complete an $n \\times n \\times n$ cube's frame, its corners and edges. We answer this problem for all $n$, and in particular show that for $n \\geq4$ one has the best po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07184","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"}