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The Mathematics of Various Entertaining SubjectsResearch in Recreational Math$
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Jennifer Beineke and Jason Rosenhouse

Print publication date: 2015

Print ISBN-13: 9780691164038

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691164038.001.0001

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Parallel Weighings of Coins

Parallel Weighings of Coins

Chapter:
(p.95) 7 Parallel Weighings of Coins
Source:
The Mathematics of Various Entertaining Subjects
Author(s):

Tanya Khovanova

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691164038.003.0007

This chapter presents solutions to generalizations of Konstantin Knop's puzzle for any number of minutes and any number of parallel scales. It first describes the similarity of the original puzzle with a multiple-pans problem: a coin-weighing puzzle involving balance scales with not two, but any number of pans. The notion of a coin's potential is defined next. The chapter then provides a solution to the parallel weighing problem in case there is an unlimited supply of real coins. Afterward, the chapter offers a solution to the original puzzle and its generalization for any number of minutes, and generalizes these results to the use of more than two scales in parallel. In addition, the find-and-label variation of this problem for any number of minutes is discussed, before the chapter concludes with a comparison of the find-and-label problem with the just-find problem.

Keywords:   coin-weighing puzzles, Knop's puzzle, parallel scales, multiple-pans problem, parallel weighing problem, find-and-label problem, just-find problem

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