Problem: With the use of three different weights, namely, 1lb.,3lb., and 9lb., 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?
Answer Choices:
A. 15
B. 13
C. 11
D. 9
E. 7
Solution:
Weights usedSinglyTwo at a time (same pan)Three at a time (same pan)Two at a time (different pans)Three at a time (different pans)TotalNo. of weighings possible3313313
or
1113=1⋅32+1⋅3+1=1310, so that the number of weighings equals the sum of the weights, when the weights are related in this manner.