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"I looked around and nobody looked like a prince even though we only have very small class member, maybe only 15-20 of us in each class," she said.
Kim said that she later noticed one student with "messy hair and tracksuits" who was often late for the early morning class, who later introduced himself as "Al".
"He was amazing, he was such a good-hearted man and we still keep good friendship. And we used to sing in the same choir so it was really great," said Kim.
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The reigning monarch of Monaco said Kim was a "brilliant student" and he said he knew at the time that she would "do a lot of good" in her life.
"She's a remarkable person, she's not only one of the most famous people in Asia and certainly in the business world but also in the charitable world and in her fight with other women leaders for women and for their engagement in society," H.S.H Prince Albert II of Monaco told CNBC Meets.
"She should be applauded for all this wonderful work that she's doing," he said.
The full program - CNBC Meets: Sung-Joo Kim - will air on CNBC Europe on Wednesday 4 June.