Mathematics – History and Overview
Scientific paper
2010-10-26
Mathematics
History and Overview
15 pages. 5 figures
Scientific paper
A problem that enjoys an enduring popularity asks: "what is the least number of pound weights that can be used on a scale pan to weigh any integral number of pounds from 1 to 40 inclusive, if the weights can be placed in either of the scale pans ?" W.W. Rouse Ball attributes the first recording of this problem to Bachet in the early 17th century, calling it "Bachet's Weights Problem". However, Bachet's problem stretches all the way back to Fibonacci in 1202, making it a viable candidate for the first problem of integer partitions. Remarkably, given the age of Bachet's problem, an elegant and succinct solution to this problem when we replace 40 with any integer has only come to light in the last 15 or so years. We hope to expound on this generalization here armed only with our sharp wits and a willingness to induct. In doing so we will discover some of the joys of partitions of integers and enumerative combinatorics. This expository article, while of interest to researchers in combinatorics, integer partitions and the history of mathematics, is written with an impressionable undergraduate audience in mind.
No associations
LandOfFree
Bachet's Problem: as few weights to weigh them all does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Bachet's Problem: as few weights to weigh them all, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bachet's Problem: as few weights to weigh them all will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-160130