Problem 2
With the use of three different weights, namely 1 lb., 3 lb., and 9 lb., how many objects of different weights can be weighed, if the objects to be weighed and the given weights may be placed in either pan of the scale?
***Clarification*** Only the three weights and the one object being weighed maybe be used (i.e. no previously weighed objects), but that doesn't mean you have to use all three weights at once. You are free to use one, two or three of the weights.
Solution
Using any number of the weights and one object we find that we may weight 13 different objects, namely objects whose weights are the natural numbers from 1 to 13.
This table shows all the different combinations possible.
| Left Hand Side | = | Right Hand Side |
| 1lb | = | (1lb Object) |
| 3lb | = | (2lb Object) 1lb |
| 3lb | = | (3lb object) |
| 3lb 1lb | = | (4lb object) |
| 9lb | = | (5lb ojbect) 3lb 1lb |
| 9lb | = | (6lb ojbect) 3lb |
| 9lb 1lb | = | (7lb object) 3lb |
| 9lb | = | (8lb object) 1lb |
| 9lb | = | (9lb object) |
| 9lb 1lb | = | (10lb object) |
| 9lb 3lb | = | (11lb object) 1lb |
| 9lb 3lb | = | (12lb object) |
| 9lb 3lb 1lb | = | (13lb object) |
