I have phrased the sentence below awkwardly, I assume:
By numbering the examples, you are a genius.
I want to know how it can be fixed to fit a proper and clear structure. And I suppose it would be more natural if it was stated like this:
You are a genius by numbering the examples.
I think of that structure as if-statements but when they actually happen, not if they were to happen, like:
If you numbered the example, you would be a genius.
Also, would "consider" fit in the sentence?
By numbering the examples, you are considered a genius.
Answer
There's certainly a valid sentence structure of the form "by [verbA] you [verbB]". It can use other prepositions, as well, such as in or through.
However, your first example is not natural. It doesn't work. I think that's because the first verb is an action verb, while the second is a stative verb.
The way to say that a person is shown to be a genius by showing the examples is to actually use words that mean that:
By numbering the examples you are shown to be a genius.
By numbering the examples you show your genius.
In numbering the examples you prove that you are a genius.
If you wanted to say that number the examples actually caused them to be, or become, a genius, you want use become:
By numbering the examples you become a genius.
For an example where both are stative:
In knowing all prime numbers less than 1,000,000, you are a genius.
But not, although it is less awkward than your example:
In knowing all prime numbers less than 1,000,000, you become a genius.
This is less awkward, and I'm not 100% sure why... perhaps the first half can be stative and the second half action, but not vice versa. However, this is not awkward:
By learning all prime numbers less than 1,000,000, you become a genius.
More confidence about what sounds awkward is likely to come with practice, rather than learning rules. English is rather lacking in consistent general rules.
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