There are 26 packages, labeled A to Z, and each is known to weigh some whole number of pounds in the range of 1 to 26. It is possible that two or more packages weigh the same amount.
(a) Determine the weight of each package with a two-pan balance and exactly four weights of your design.
(b) Now do it with exactly three weights.
The obvious answer to the 4 weight question is to use numbers that either added or subtracted total all the numbers from 1 to 26. The logical set for this is 1,3,9,27
The key to the three weights question is realising that you do not need to know everything to interpolate between points. You only need to know even numbers since you can measure parcels and determine the odd numbers by knowing that the higher even number tips the scales one way whilst the lower ever number tips it the other. This leads you to start from 2 and come up with the set 2,6,18
Voila!
Solution
