Problem of the
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.
Fifth Week, March 6. Paul and Simon.
(I heard of this problem from B. Ganter.)
- 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?
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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Updated Mar 6, 2000