<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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 2<sup>k</sup> coins in k + 1 weighings, which is better than any strategy for a 3-way scale.</p></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.

The 5-Way Scale

Recreational Mathematics Magazine

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"The 5-Way Scale"}

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...

The 5-Way Scale

Published Online: Oct 11, 2019

Page range: 5 - 14

DOI: https://doi.org/10.2478/rmm-2019-0001

Keywords
coin weighings

© 2019 Tanya Khovanova et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

The 5-Way Scale

Published Online: Oct 11, 2019

Page range: 5 - 14

DOI: https://doi.org/10.2478/rmm-2019-0001

Keywordscoin weighings

© 2019 Tanya Khovanova et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
coin weighings