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.

It seems to me that if you started with wieghts of 1lb, 2lb, 4lb, and 8lb you could find all the packages that weighed from 1 to 15 lbs.  Then you could use the already weighed packeges in addition to the weights to weigh the remaining packages.  Once you found a package wieghing 16 lbs (or a combination of packages totalling 16 lbs) you would have no problem finding the weight of the rest of the packages.

Unless, of course, all of the packages were OVER 15 lbs.

The same method would apply for three weights as long as the packages are not ALL over 7 lbs.

Posted by Sing4TheDay on 2005-06-28 15:40:13