Problem of the Week

In this space, I will try to post an interesting and challenging puzzle or short problem every week. I am giving these problems to my classes for their mathematical entertainment. Some of the weekly puzzles I invented myself, but many are scavenged from other sources. If you would like to contribute a problem, please email me. Enjoy!

### Fifth Week, March 6. Paul and Simon.

• Simon: "I know the sum S of two integers greater than 1, but not their product."
• Paul: "I, on the other hand, know the product P of the two numbers, but not their sum."
• Simon thinks about the number S and replies, "I believe you, because you cannot calculate S from P, no matter what value P may have."
• Paul thinks for a while and then announces, "Now I know S."
• "How nice," replies Simon, "now I also know P."
• Paul adds, "And moreover, S has the smallest value that is possible, given our conversation."
• What are the values of P and S?
(I heard of this problem from B. Ganter.)

Note: I am not giving out solutions to "Problems of the Week". But I am very happy to discuss these problems with you, including any partial or attempted solutions that you might have. I am always interested in hearing about interesting or creative solutions, so let me know if you have any!

See previous Problems of the Week.

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Peter Selinger / Department of Mathematics and Statistics / Dalhousie University
selinger@mathstat.dal.ca / PGP key
Updated Mar 6, 2000