Answer to Puzzle Contest (from the winner):

"You need 3 weights: 1#, 3#, 9#.

To weigh X, where X is 
  X Lpan Rpan

  1 1# X
  2 3# X,1#
  3 3# X
  4 3#,1# X
  5 9# X,1#,3#
  6 9# X,3#
  7 9#,1# X,3# 
  8 9# X,1#
  9 9# X
 10 9#,1# X
 11 9#,3# X,1#
 12 9#,3# X"

A few people also pointed out that these 3 weights will measure objects up to 13 pounds. A few others pointed out (or gave as their sole answer, which was counted as correct), that you can weigh all 12 with a 1, 3, and 8 pound set. Here is an explanation of such from Andy Muenz, Glenolden, PA:

" Left Side Right Side
Object
1lb 1lb weight
2lb + 1lb weight 3lb weight
3lb 3lb weight
4lb 3lb weight + 1lb weight
5lb + 3lb weight 8lb weight
6lb + 3lb weight 8lb weight + 1lb weight
7lb + 1lb weight 8lb weight
8lb 8lb weight
9lb 8lb weight + 1lb weight
10lb + 1lb weight 8lb weight + 3lb weight
11lb 8lb weight + 3lb weight
12lb all 3 weights"

Also, Gus Molina and Shirley Wolf pointed out that in addition to these two methods, a THIRD method exists: a 2, 3 and 9 pound set. Only these 3 sets were found. Can you find any others?

Winner: Al Siller, Rockville, MD

Contest Statistics: 20 answers submitted, 10 answers correct, 50.00% accuracy. Chance of a correct answer winning: 10.00%.