[net.math] sum product puzzle

bek@duke.UUCP (Barrett E. Koster) (07/24/84)

I have a puzzle (an old unsolved favorite of mine) which was
rumored to have been discussed recently here.  I don't mean
to restart the discussion, but my news log doesn't go back far
enough to find it, and I would like very much to see a solution.
(If the puzzle is not in fact old to this group, then you all
can just take a crack at it now.)
 
Person A thinks of two integers between (but not including) 1 and
100.  A hands the sum of the two numbers to a person we shall
call S, and the Product to a person we shall call P.  The following
conversation takes place:
S: I don't know what the numbers are.
P: I don't know what the numbers are, either.
S: I knew you didn't know.
P: Oh, well, in that case, I DO know what they are.
S: In that case, so do I.

The question is, what were the two numbers?

Barry Koster      duke!bek