Closely related to the representation of integers in different bases is
the idea of
representing integers as sums and differences formed from a given
system of fixed
integers. This is what happens in a two-pan balance scale, where the fixed
integers are
weights with known values. The object of unknown weight, below, is Lollapallooza,
a
huge professional wrestler. The ten fixed weights which you are allowed to
use on either
pan are
A = 1, B = 3, C = 8, D = 25, E =
75, F = 225, G = 654, H = 1981, I = 5945,
J = 17835
To remove a weight from a pan, highlight a letter from A to J
on LeftPan or RightPan
and type 0 (zero). To place a weight on either pan highlight any position
except Lollapallooza and type a capital letter from A
to J. Be sure that any letter appears on the scale at most once. The goal, of course, is
to determine the weight of Lollapallooza
(in ounces).