"You have used a cumbersome method to solve this question.I would not / will not use it."
Which of above two(would and will) is preferrable to use? Can would not be used above to politely refuse?
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Both are correct, but mean different things.
1) I will not use it.
expresses the speaker's determination not to use the method his/her interlocutor has used.
2) I would not use it.
can express the same idea as (1), though in a less categorical form. However, in this context in which the interlocutor's attitude has been described, it will most likely mean:
2') I would not use it if I were you.
Therefore, (2) expresses criticism about the interlocutor's use of the method and the speaker's hypothetical adoption of a different approach.