Solution to "The Scale Puzzle"

Puzzle #1: Use four weights of 1, 2, 4 and 8 pounds. Any value from 0 to 15 can be formed by a suitable combination.

Puzzle #2: Use weights of 1, 2, 4, ..., 2^k-1. Every value from 0 to 2^k-1 can be formed. For instance, if the maximum weight is 63 = 2^6 - 1, then we use six weights of 1, 2, 4, 8, 16 and 32 pounds.

Puzzle #3:

Puzzle #4: Use weights of 1, 3 and 9 pounds. Consider the following:

         0 = 0
         1 =       + 1
         2 =   + 3 - 1
         3 =   + 3
         4 =   + 3 - 1
         5 = 9 - 3 - 1
         6 = 9 - 3
         7 = 9 - 3 + 1
         8 = 9     - 1
         9 = 9
        10 = 9     + 1
        11 = 9 + 3 - 1
        12 = 9 + 3
        13 = 9 + 3 + 1
      

Puzzle #5:

Back to The Scale Puzzle.