The 5-Way Scale

2019/03/08 by Tanya Khovanova, Joshua Lee, Khovanova, Tanya +1
Mathematics · #00A08 #05A99 #Combinatorics (math.CO) #FOS: Mathematics #History and Overview (math.HO) #math.CO #math.HO #msc:00A08 #msc:05A99

paper · pdf · doi:10.48550/arxiv.1903.04900

9 pages

arxiv created 2019/03/08 · arxiv updated 2019/03/13

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 2^k coins in k+1 weighings, which is better than any strategy for a 3-way scale.

Related

• Counting Counterfeit Coins: A New Coin Weighing Problem
• Solution to the Counterfeit Coin Problem and its Generalization
• Coins that Change Their Weights
• Coins of Three Different Weights
• Discreet Coin Weighings and the Sorting Strategy