How to say the professor solved the problem at last. in Japanese

1)教授教授(kyouju) (n,vs,adj-no) professor/teaching/instruction(int) indicating a subject/yes/indeed/well/ha!/what?/huh?/sighついにそno dictionary result, likely a conjigated verbの(no) (prt) indicates possessive/nominalizes verbs and adjectives/substitutes for "ga" in subordinate phrases/indicates a confident conclusion/ indicates emotional emphasis/indicates question問題問題(mondai) (n) problem/questionを(wo) (prt) indicates direct object of action/indicates subject of causative expression/indicates an area traversed/indicates time over which action takes place/indicates point of departure or separation of action/indicates object of desire, like, hate,解きno dictionary result, likely a conjigated verbno dictionary result, likely a conjigated verb明か明か(akiraka) (adj-na) clear/fresh/brightしたした(shita) (n) did/a past form of the previous verb/tongue/tongue-like object/clapper/talon。(。) Japanese period "."    
kyouju hatsuinisono mondai wo toki akiraka shita 。
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