Two Numbers Puzzle-Asked in Amazon interviews.

Question:

Ben has 2 integers. He tells sum of the integers to the person S and product of those numbers to P.Now there is this conversation between S and P.

S: I don’t know what the numbers are

P: Neither do I

S: Now, I know what the numbers are.

P: Hey, me too.

Assuming S and P to be very wise and good in mathematics, What are those two integers?

Solution: The two numbers are 2 and 2.

S would have got 4, which means 1 + 3 or 2 + 2. so that’s why he was not sure of the numbers.
P would have also got 4, possibilities 14 and 22.
Now, had the numbers be 1 and 3, P would have got 3 and he would have been sure of the numbers, but that was not the case, So S became sure that numbers are 2 and 2.
Now, P knows that numbers cant be 1 and 4, because there are two possibilities of getting the sum as 5, 1+4, 2+3, and in both these cases S cant guess the number depending on P’s earlier answer, as for both product 4 and 6 there are more than 1 possibilities.
Thus P also knows that the numbers are 2 and 2.

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