Hopefully you are only interested in integer weights. Hopefully this is correct (question wise):
There are 30 weights. 1 g to 30 g. He wants you to construct a scale that can measure from 1 g to 40 g by using ONLY 4 of the original 30 weights.
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Assuming all the "weights" only go on one side while the "object" goes on the other, this is clearly not possible as the max weight goes upto only 30g.
1g and 2g must be there. The other 2 must add up to 37g. Also, 3g or 4g must be present to "measure" 4g. Clearly, this weight system will not be possible - putting weights on one side with the object on the other.
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The other approach is to "measure" weights by being able to put weights on both sides. For example, in the above mentioned scenario, you don't need a 3g or a 4g weight to measure 4g. You can use a 5g or a 1g weight. Just put the 1g with the "object" and put the 5g on the other side and see if it balances.
Anyways, I am not gonna think about think problem more until the poser of the question clarifies by original intepretation.
a IQ question 
Linear Mode
