There is a one person who have two numbers, he tells sum to the person S and product of those numbers to P.

Now there is this conversion between S and P.

S: I don’t know what are the numbers.

P: I also don’t know what are the numbers.

S: Now i know what are the numbers.

P: Now i also know what are the numbers.

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

Note: Numbers are greater than 0.

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 1*4 and 2*2.

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.

Sahil Pareek says

When 1st says i don’t know that illustrates the sum is greater than 3;

when 2nd says i don’t know that illustrates the number is not a prime number;

Since as the turn of 1st comes again, he knew the answer this implies that there were only 2 combinations of sum possible previously and now he eliminated one of the pair whose product comes out to be prime, so he left with one. Since the 2 combinations are only possible if :

Sum =4; pairs are (3,1) and (2,2) and one of the pairs multiplication answer is 4 which is not prime.

So, the answer is (2,2).

Saket says

Even 1 and 4 just works fine on the same logic.

Gurbakhsish Singh says

I think the question is incorrect and so is the answer, please look into this for the original question and a logical answer http://www.qbyte.org/puzzles/p003s.html

srikar says

its 2 and 2 , sum is 4 and it can be divided into 3,1 and 2,2 but 4 has two sets of products so p is not sure

rishi says

1 and 2

Amit says

why it cant be 4 and 5

krishna says

how?

Raghava G D says

the two numbers are 2 and 2.