“It drove you crazy to teach her, but we could not get mad at her,” said Lee Chang-su, another teacher. “She was always cheerful. She still had the little girl in her.”

It was only last November, on her 950th try, that she achieved a passing grade of 60 out of 100. She then passed two driving skill and road tests, but only after failing each four times. For each of her 960 tests, she had to pay $5 in application fees.

“I didn’t mind,” said Ms. Cha. “To me, commuting every day to take the test was like going to school. I always missed school.”