Yesterday, we looked at a problem involving a spice trader and his weights. Today,

*you*are going to be the spice trader.

Imagine you have a four-pan balance, as illustrated below. The two outer pans are twice the distance from the fulcrum as the inner pans, the whole arrangement being balanced at the start.

You have a set of weights calibrated to be whole number ounces but you really don't want to carry them all with you. You wish to be able to weigh every amount between 0.5 to 32 ounces inclusive, going up in steps of 0.5 ounces, and to do so in one weighing.

What set of weights should you take, given that you want the smallest number of weights and the smallest sum of their weights?

Is your answer unique, or is there more than one solution?

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