You have a double pan balance scale on which you can place weighted objects on both sides. For example, if you have two objects, one with weight 5 and one with weight 7, you can measure items of weight 5, 7, or 12. You can also measure items of weight 2, by placing 7 on one side and 5 on the side which contains the object to be weighed. If the scale balances, you know that the item has weight 2 since 5+2=7.

[3 points] Suppose you have six objects, with weights 1, 2, 4, 8, 16, 32. Clearly explain how you can use the balance scale to measure an item of weight N, where N is any whole number between 1 and 50.

Solution:

[4 points] Suppose you have three objects with weights 1, 3, and 9. I claim that there is a value X such that you can use the balance scale to weigh any item of a whole number weight from 1 to X? Determine the value of X and provide a brief justification as to why you can

weigh each number in the range and nothing larger.