问题

Dr. Chen is organizing a number guessing game in his Math Pr


Dr. Chen is organizing a number guessing game in his Math Problem Solving class. Three smart students Adam, Ben and Wukong are the participants. They need to find two numbers $x$ and $y$, such that $1<x<y<10$. Dr. Chen gives the sum $x+y$ to Adam, the product $xy$ to Ben and the sum $x+y+xy$ to Wukong. The 3 students are asked to write down their answer if they know. But no one knows what $x$ and $y$ are. After knowing that no one knows the answer in the first round, all of the 3 students know the correct answer in the second round. What are these two numbers $x$ and $y$? Show your reasoning.

已解决 · 高中数学
提问于2023年05月04日 · 阅读 48

解答

Ben知道两个数的积却不知道两个数,说明这两个数的积能写成另一对数的积,只能是其中某一对26、34、46、38、29、36
Wu知道xy+x+y=(x+1)(y+1)-1却不知道两个数,说明两个数各加1后的积能写成另一对数加1的积,可以排除26、34、46、38、36,
最后剩下的是29


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