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.

Using the weights 3 5 9 and 16 you can place them on either side of the balance in various ways to net from 1 to 25 pounds so you can determine the weight of each package.

1=9-5-3
2=5-3
3=3
4=9-5
5=5
6=9-3
7=16-9
8=3+5
9=9
10=16-9+3
11=16-5
12=3+9
13=16-3
14=5+9
15=16-9+5+3
16=16
17=3+5+9
18=16+5-3
19=3+16
20=16+9-5
21=5+16
22=16+9-3
23=16+9+3-5
24=3+5+16
25=9+16
26=heavier than 25
 

Posted by Lisa on 2005-06-28 16:15:56