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Anton's Problem

Once there were 3 friends (Anton, Simon, Paul) chatting to each other in a dining hall.

The following happened:

Anton:
I've chosen two natural numbers which are both greater than 1. I'm going to tell Simon the sum and Paul the product of these numbers.
Anton then gave Simon the sum and Paul the product, such that each of our friends knew "his" number only but not the number of the other friend.
Anton:
Now, can you guess the numbers which I have in mind?
Simon and Paul liked this sort of game. Their conversation was the following:
Simon:
I don't know Anton's numbers.
Paul:
I don't know them either.
Simon:
Hey, now I know.
Paul:
Then I know them too.
A maths professor had observed this whole situation from the very beginning. He went to our friends and said:
Professor:
I know Anton's numbers, too!

Now, what are Anton's numbers?
« July 2024 »
July
MoTuWeThFrSaSu
1234567
891011121314
15161718192021
22232425262728
293031