In Scale Puzzles 103, we learned that you can use only ten weights to add up to any number of ounces up to 1,023. (If you have not yet solved that puzzle, please click here and solve it first.) In SP103, all weights were placed on one side of the scale, while the object was placed on the other.

In SP202, I challenge you to find seven different weights that will allow you to use a balance scale to weigh an object weight from one ounce up to 1,093 ounces. For this puzzle, you may place the weights on one, or both, sides of the balance scale. If you put a 3-ounce weight on one side of the scale, and it balances with a 1-ounce weight and something else, then the "something else" weighs 2 ounces. (3=2+1) or (3-1=2).

What seven weights do you need in order to measure any weight up to 1,093 ounces?

• Obviously, we need a one-ounce weight.
  Write down one (1)
• Can you calculate two with any combination of numbers on your list (1)? No, you can't. Here's how to calculate what your next weight needs to be:
  • Add the number you want to make (two) plus all the numbers already on your list (1).
  • 2+1=3
  • Write down 3
• One & three ounce weights will allow us to weigh any amount up to four ounces:
  • 1 = 1
  • 2 = 3 - 1
  • 3 = 3
  • 4 = 3 + 1
• Five is the next number we need to calculate. Use the same method that we used above.
• Keep doing this until you see a pattern.