by Susan Bricket and John Owen
Published November 3 2019 (link)
We were wondering why ancient Egyptians chose to represent arbitrary fractions as sums of distinct unit fractions of the form 1/n (thus 5/7 = 1/2+1/5+1/70). One of us recalled long ago watching our greengrocer use four brass weights of 1/2, 1/4, 1/8, 1/16 lb to weigh any number of ounces up to 15 by stacking some of them on one side of her balancing scales. We wanted to make a metric equivalent, a set of distinct weights of unit fractions of a kilo, each weighing a whole number of grams, to weigh in 10g steps up to 990g.
Naturally, we wanted to use as little brass as possible, but we found that there were several possible such sets. Of these, we chose the set containing the fewest weights.
List, in increasing order, the weights in our set.