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# balancing weights

## Question

You have an unlimited supply of 7 and 11 pound weights. You also have a 5 pound potato. Can you weigh the potato on a balance scale? What about a 9 pound potato?

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Yes. 5,7,9, and 11 are all relatively prime. Hence the equations 5+7x=11y and 9+7x=11y both have integer solutions.

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1. Place an object to be weighed on the left pan.

2. Put two 11 pound weights on the right pan (22 pounds total) and three 7 pound weights on the left pan (21 pounds total) so you get net 1 pound added to the right pan, and place one tally mark on a sheet of paper.

3. Repeat step #2 until the balance is even, and the number of tallies will be the weight of your object.

But this is not the approach with the minimum number of weights, in case anyone wants to go after that problem.

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