peter, simon and daniel are given the task to figure out two numbers. they get the following information: both numbers are between 1 and 1000 and whole numbers (no decimal numbers). peter is given the result of multiplying both numbers with each other (= the product), simon is given the sum of both numbers (= one number plus the other), and daniel is given the difference between both numbers (= one number minus the other).

however, they must not share those pieces of information with each other. but all three guys are mathematical geniuses, they can do any number of calculations in their head instantly.

then, the following conversation takes place:

peter: i don't know the numbers.

simon: you don't need to tell me that, because i knew that already.

peter: in that case, i know both numbers now.

simon: ok, i know them now too.

daniel: i still don't know the numbers. i can only guess a number, which is probably one of the numbers we're looking for, but i don't know for sure.

peter: i know which number you're talking about, but that one is wrong.

daniel: ok, then i also know both numbers now.

simon: you don't need to tell me that, because i knew that already.

peter: in that case, i know both numbers now.

simon: ok, i know them now too.

daniel: i still don't know the numbers. i can only guess a number, which is probably one of the numbers we're looking for, but i don't know for sure.

peter: i know which number you're talking about, but that one is wrong.

daniel: ok, then i also know both numbers now.

which are the two numbers?