Figuring out Primary/Secondary/Tertiary Structures

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Homework Statement



In general, when presented with a problem such as write out all the primary alcohols/amines/ketones/aldehydes with this formula ________, how do I actually go about systematically figuring them out? I have seen problems with up to 8 different structures for me to figure out. How in the world do I figure it out without wasting my time drawing out a million different structures?
 
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I am not aware of any purely systematic way. If they exist, they are buried deep in a graph theory.

My approach would be to start with a straight chain, then to move one carbon around, then to move two carbons around and so on.

If it makes you happy - I have never seen such questions asked on a serious exam, they are more like a step in building your awareness of all possible isomers existing in general.