ark@rabbit.UUCP (06/07/83)
I have picked two integers between 3 and 100 (inclusive), and given their sum to Sally and their product to Paul, both very clever mathematicians. After suitable time for thought, Sally says to Paul: "It is impossible for you to figure out my sum." After more time for thought, Paul replies: "I have figured out your sum." After still more thought, Sally says: "I have figured out your product." What are the two numbers? Hints: (1) this problem is completely legitimate. I have left nothing out, and there are no tricks. (2) there is no other communication between Sally and Paul. (3) their statements are all true. There is enough information here to solve the problem. The solution is unique in integers <= 100. It may be unique over all integers.