THETA DIVISION

Question 7

Number Theory★★★Question Bank

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Question

A balanced scale is available to weigh packages which may weigh from

1

lb to

9

pounds, inclusive. All packages have integral weights. If you can use a

1

lb, a

3

lb, and/or a

5

lb weight on either plate of the scale, in addition to the object to be weighed, how many distinct pound weights

\{1,2,\ldots,9\}

of packages can you accurately determine? (Note: the weights can be put on either or both plates of the scale.)

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