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.
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 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.