1. bookVolume 6 (2019): Issue 11 (September 2019)
Journal Details
License
Format
Journal
eISSN
2182-1976
First Published
16 Apr 2016
Publication timeframe
2 times per year
Languages
English
access type Open Access

The 5-Way Scale

Published Online: 11 Oct 2019
Volume & Issue: Volume 6 (2019) - Issue 11 (September 2019)
Page range: 5 - 14
Journal Details
License
Format
Journal
eISSN
2182-1976
First Published
16 Apr 2016
Publication timeframe
2 times per year
Languages
English
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.

Keywords

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[4] Li, A. “On the conjecture at two counterfeit coins”, Disc. Math., 133, 301–306, 1994.10.1016/0012-365X(94)90038-8Search in Google Scholar

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