Non-standard Weights

Logic Level 2

You have a pan balance, and two weights of 1 kg,4 kg1\text{ kg}, 4\text{ kg} and 16 kg16\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 kg4\text{ kg} weight on one pan, and a 1 kg1 \text{ kg} weight on the other pan. Only an object weighing 3 kg will be able to balance the pans.

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