Balance Power

Using balancing scales what is the least number of weights needed to weigh all integer masses from 1 to 1000? Placing some of the weights in the same pan as the object how many are needed?
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Problem



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Balance Power
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?