  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.
