{"paper":{"title":"Solution Numbers for Eight Blocks to Madness Puzzle","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.DM","math.HO"],"primary_cat":"math.CO","authors_text":"Erika Roldan, Inga Johnson","submitted_at":"2024-07-18T06:44:48Z","abstract_excerpt":"The 30 MacMahon colored cubes have each face painted with one of six colors and every color appears on at least one face. One puzzle involving these cubes is to create a $2\\times2\\times2$ model with eight distinct MacMahon cubes to recreate a larger version with the external coloring of a specified target cube, also a MacMahon cube, and touching interior faces are the same color. J.H. Conway is credited with arranging the cubes in a $6\\times6$ tableau that gives a solution to this puzzle. In fact, the particular set of eight cubes that solves this puzzle can be arranged in exactly \\textit{two}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.13208","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/2407.13208/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"}