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You can weigh all integer masses from 1 to 60 with 6 weights
putting the weights in one pan and the object in the other pan.
Which weights are used?
What about weighing all integer masses from 1 to 1000 or from
1 to n?
How many weights are needed if you put weights in both
pans?

The first part of an investigation into how to represent numbers using geometric transformations that ultimately leads us to discover numbers not on the number line.
This article for the young and old talks about the origins of our number system and the important role zero has to play in it.