You have a pan balance, and two weights of \(1\text{ kg}, 4\text{ kg} \) and \(16\text{ kg}\) each.

How many different positive weights can you measure using just these given weights?

As an explicit example, it is possible to measure 3 kg using these weights. Place a \(4\text{ kg}\) weight on one pan, and a \(1 \text{ kg}\) weight on the other pan. Only an object weighing 3 kg will be able to balance the pans.

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