{"paper":{"title":"Confirming the Labels of Coins in One Weighing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.HO","authors_text":"Akhil Kammila, Alicia Li, Anish Mudide, Isabel Tu, Isha Agarwal, Jeffrey Shi, Kaylee Ji, Maya Smith, Patrick Chen, Paul Braverman, Shane Lee, Tanya Khovanova, William Du","submitted_at":"2020-06-30T16:05:50Z","abstract_excerpt":"There are $n$ bags with coins that look the same. Each bag has an infinite number of coins and all coins in the same bag weigh the same amount. Coins in different bags weigh 1, 2, 3, and so on to $n$ grams exactly. There is a unique label from the set 1 through $n$ attached to each bag that is supposed to correspond to the weight of the coins in that bag. The task is to confirm all the labels by using a balance scale once.\n  We study weighings that we call downhill: they use the numbers of coins from the bags that are in a decreasing order. We show the importance of such weighings. We find the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.16797","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/2006.16797/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"}