What Are the Two Numbers in the Sum and Product Puzzle?

[mite]

Homework Statement

There are two unknown numbers each between 2 & 99 person 'P' is told the product and person 'S' is told the sum when asked about the two numbers their conversation is as follows
P-I don't know them
S-I knew that already
P-Then I know the two numbers
P-Then I know them too
Using these clues we have to find the two numbers

Homework Equations

I don't know

The Attempt at a Solution

I have no idea. Can anyone please give me some clue how to solve this.I don't want solution only some clue to solve.

 

[cheff3r]

okay i got given this question a while back i will start you off, youve got think about all the basic logic parts to adding/multiplying, so i will start you off and then well see weather you can get any further

From p "I do not know the numbers", we can deduce that the product is not the product of two primes. If it were, then Product would have been able to factorize the product into two primes, and would then know the two numbers.

From s "I knew you didn't knew the numbers" we can deduce that the sum must be an odd number, because every even number (at least for small numbers) can be written as the sum of two primes (Goldbach's Conjecture). The only way for S to know that p doesn't know the numbers, is for the sum to be an odd number.

 

[Architeuthis Dux]

I would approach this problem by first considering the given information and trying to understand the logic behind it. From the conversation between P and S, it seems that knowing the product and sum of the two unknown numbers was not enough for either of them to determine the individual numbers. However, after sharing their knowledge with each other, they were both able to determine the numbers.

One possible approach to solving this problem could be to create a system of equations using the given information. We know that the numbers are between 2 and 99, so we can start by creating two equations with two unknowns that fit within this range. For example:

x + y = sum
xy = product

From here, we can use algebraic methods to solve for the two numbers. However, this may not be the most efficient approach and there may be alternative methods or strategies to solve this problem. It would also be helpful to think about the properties of multiplication and addition that may be relevant in this situation.

Additionally, it may be helpful to consider different scenarios and test them out to see if they fit the given information. For example, if the sum is a prime number, what does that tell us about the individual numbers? Or if the product is a perfect square, what does that tell us?

Overall, this problem requires critical thinking and problem-solving skills. It may also be helpful to discuss with others and collaborate on possible solutions.