James the Mathematician wants to find a partner for a serious relationship. He has his own scoring system. He talks with N out of 100 girls, rejects them and records the best score S. He decides to talk to all 100 girls, making a decision about each one immediately. Once rejected, a girl cannot be recalled. After that, he continues to talk to others and stops when the girl has a score better than S.
What number N do you recommend to the boy?