"I don't know the numbers": a math puzzle · Caffeinspiration

I saw a math puzzle the other day on Hacker News. It reads as follows: Two numbers are chosen randomly, both are positive integers smaller than 100. Sandy is told the sum of the numbers, while Peter is told the product of the numbers. Then, this dialog occurs between Sandy and Peter: Peter: I don’t know the numbers. Sandy: I don’t know the numbers. Peter: I don’t know the numbers. Sandy: I don’t k

[ABA]

1～100の数を2つ選んで、一人にはその和を、一人にはその積を教えて、二人に交互に「2つの数は何でしょう？」と聞いたところ、二人が7回「分かりません」と答えた後、一人が「分かりました」と答えた。2つの数は何？