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.
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).
Even 1 and 4 just works fine on the same logic.
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
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
1 and 2
why it cant be 4 and 5
how?
the two numbers are 2 and 2.