1) He will be the first one who solves that problem
or
2) He will be the first one to solve that problem.
Number 2 is better.
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as far as i know,the second one is the correct one
because the first one is written with present simple, whereas the subject He will be,which is the future simple tense
it hasn't happened yet,so can't use the first sentence
if i'm wrong,then sorry :''0