论文标题
在一个称重中确认硬币的标签
Confirming the Labels of Coins in One Weighing
论文作者
论文摘要
有$ n $ bags带有硬币的袋子看起来相同。每个袋子都有无限数量的硬币，所有袋子中的所有硬币都重量相同。不同袋中的硬币重量为1、2、3，依此类推，至$ n $ grams。每个袋子附加了一个唯一的标签，该标签应与该袋中的硬币的重量相对应。任务是通过使用余额量表确认所有标签。 我们研究了我们称为下坡的称重：他们使用袋子中的硬币数量的数量，这些硬币数量减少了。我们表明了这种称重的重要性。我们发现在下坡的称重中，硬币的总重量最小，可以证实袋子上的标签。我们还发现了这种称重所需的最小硬币的界限。
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.
