轉貼美國卡內基美隆大學數學研究問題

感謝交大電機系楊谷洋教授熱心提供這則取自美國卡內基美隆大學的數學研究問題。

Homer gives mathematicians Patty and Selma each a different integer, not known to the other or to you. Homer tells them, within each other’s hearing, that the number given to Patty is the product ab of the positive integers a and b, and that the number given to Selma is the sum a+b of the same numbers a and b, where b>a>1. He doesn’t, however, tell Patty or Selma the numbers a and b. The following (honest) conversation then takes place:

Patty: “I can’t tell what numbers a and b are.”

Selma: “I knew before that you couldn’t tell.”

Patty: “In that case, I now know what a and b are.”

Selma: “Now I also know what a and b are.”

Supposing that Homer tells you (but neither Patty nor Selma) that neither a nor b is greater than 20, find a and b, and prove your answer can result in the conversation above.

Credit This problem comes from the Carnegie Mellon Math Studies Problem Seminar. 

這是參考解答↓ 

http://www.usamts.org/Solutions/Solution4_1_17.pdf

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