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Re: Very interesting problem (~number theory...)
Posted:
Nov 12, 1999 3:27 PM
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> Definiton 4. A sum S is said to be a perfect sum if it is
> a good sum, and all pair Ps are good products.
>
> So, if S is even, it can not be perfect, since
> any even number can be the sum of 2 prime numbers (
> at least for <200 integers); and the product of 2
> prime numbers is not good product.
Actually this may be true but cannot be relied upon here because the set of
primes we use can only include those <101. The numbers 182, 188, 192, 196,
and 200 are all possible sums for which Miss Sum could still make her first
statement.
I wrote a Matlab program (which runs for 45 minutes on a Pentium 133 :P ) to
solve this problem. There is only one solution for the set 1 to 101, and it
is (4,13) as someone already said. Somewhere later in this thread someone
mentioned (67, 82) but I could not tell if they were claiming that was a
solution to this problem or a solution to another person's solution which
therefore discredited that solution?
I'd be happy to share the program if anyone would like to see it.
>
> >
> > A man thinks of two natural numbers greater than 1 and less than 101
> > (strictly).
> > He tells the sum of these two numbers to Miss Sum and the product to Mr
> > Product.
> > Then Mr Product says: "I don't know what numbers are".
> > Miss Sum: "I already knew that you could not know them"
> > Mr Product: "Now I know what numbers they are"
> > Miss Sum: "I know them too!!!"
> > What are the two numbers?
>
--
joshua_parsell@hotmail.com
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