# 4-Panned Balance

Logic Level 5

You have a balance with fulcrum at $$(0,0)$$ and pans at $$\left(\pm1,0\right)$$, $$\left(\pm2,0\right)$$ (as shown in the diagram). Find the least number of positive integer weights you need in order to measure any integer weight from 1 to 1000. Note that any number of weights can be placed in any of the 4 pans (even the pan with the object you want to weigh).

Clarification: You want to be able to weigh the integer weights from 1 to 1000, but you should not assume that the object you weigh will have an integer weight.

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