五种量表

Recreational Mathematics Magazine Pub Date : 2019-03-08 DOI:10.2478/rmm-2019-0001

T. Khovanova, Joshua Lee

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摘要

摘要本文讨论了硬币称重问题，该问题使用五向刻度，该刻度有五种不同的可能结果:MUCH LESS, LESS, EQUAL, MORE和MUCH MORE。5路量表比常规的3路量表提供了更多的信息。我们研究的问题是从一堆看起来一样的硬币中找出两个假硬币在最小数量的加权使用五向标度。我们讨论了五向量表和三向量表的异同。我们引入了一种5向量表的策略，它可以在k + 1加权的2k枚硬币中找到假币，这比任何3向量表的策略都要好。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The 5-Way Scale

Abstract In this paper, we discuss coin-weighing problems that use a 5-way scale which has five different possible outcomes: MUCH LESS, LESS, EQUAL, MORE, and MUCH MORE. The 5-way scale provides more information than the regular 3-way scale. We study the problem of finding two fake coins from a pile of identically looking coins in a minimal number of weighings using a 5-way scale. We discuss similarities and differences between the 5-way and 3-way scale. We introduce a strategy for a 5-way scale that can find both counterfeit coins among 2k coins in k + 1 weighings, which is better than any strategy for a 3-way scale.

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