2020/06/30 by Isha Agarwal, Agarwal, Isha, Paul Braverman +23
Computer Science · Mathematics · #00A08 #05A17 #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #History and Overview (math.HO) #math.CO #math.HO #msc:00A08 #msc:05A17
paper · pdf · doi:10.48550/arxiv.2006.16797
23 pages
arxiv created 2020/06/30 · openalex publication_date 2020/06/30 · arxiv updated 2020/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. 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 smallest possible total weight of coins in a downhill weighing that confirms the labels on the bags. We also find bounds on the smallest number of coins needed for such a weighing.