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.

(In reply to Using 4 weights by Lisa)

Interesting solution, although I think I came up with a simpler method.  You can completely ignore the odd numbers, and just cover the even numbered weights which can be done with weights of 2lbs., 4 lbs., 8lbs., and 16 lbs., i.e.:

If it's less than the two-pounder, you can assume the bag weighs one pound.

If it's greater than the two-pounder, but less than the four-pounder, you can assume the bag weighs three pounds.

four-pounder + two-pounder = six pounds

eight-pounder

eight-pounder + two-pounder = ten pounds

eight-pounder + four-pounder = twelve pounds

eight-pounder + four-pounder + two-pounder = fourteen pounds

sixteen-pounder

sixteen-pounder + two-pounder = eighteen pounds

sixteen-pounder + four-pounder = twenty pounds

sixteen-pounder + four-pounder + two-pounder = twenty-two pounds

sixteen-pounder + eight-pounder = twenty-four pounds

sixteen-pounder + eight-pounder + four-pounder + two-pounder = twenty-six pounds

Posted by The King on 2005-06-29 16:11:25