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Title
The 5-Way Scale
Authors
Joshua Lee, Tanya Khovanova
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
coin weighings
Milestones
Published: 2019/10/14
Author Details
Joshua Lee
jlee2022@mit.edu
MIT

Tanya Khovanova
tanya@math.mit.edu
MIT

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