Can you guess the numbers?

[Hussanal Faroke]

is the answer correct!

[The_Big_K]

Nope

No right answer yet.

[Hussanal Faroke]

Pls tell me,what is wrong with the soln

[The_Big_K]

Hmm. I read your explanation. Could you now explain; with your answers, how the dialog between Ash & MaRo is valid?

[Hussanal Faroke]

Ash get 7 as sum. So the possible slns are (5,2) and (4,3). so he said "I can't determine what are these numbers".
MaRo get 12 as product.so the possible slns are (6,2) and (4,3). so the possible sum for a&b are 8 or 7. Even the sum is 7 or 8, we can generate that sum in two or more ways. So with confidence he said that "Ah, i knew you wouldn't be able to do this".
Ash already know the sum is 7.If the soln is (5,2) maro can easily tell the soln.Because there is no more feasible sln to generate aproduct of 10.
so he got the soln as (4,3).
if the sum is eight ash can't get the correct soln. because the feasible sln for
sum=8 are (4,4),(3,5),(2,6). He can never reach a sln.
From this Maro get the soln.ie(4,3).

[jejt]

First time poster..

Using the rules and set theory (and a database of the possible answers)

1 < x
1 < y

x + y < 100

and that one person knows x+y and the other knows x*y, and that each knows the other can't work out the solution, gives us the following:

There are 2352 possible number combinations. Of these, we can ignore 2 because they allow the person who knows the sum to work it out straight away (i.e. 4 and 5) and 606 more that the product guy would be able to work out straight away (multiples of two primes e.g. 17*17 can only be 17*17).

Of the sets of solutions which are in a group of two, there are just two from the point of view of the sum - those that create the product answer of 6 and 7. (for the product, theres a large group of 2 answers).

If the answer had been 6, then the pairs would have been 2,4 or 3,3. 2,4 is the product of 8, which only has one option (so is instantly solvable), as well as 3,3 (being the product of two primes) also removing it as an option.

If the answer had been 7, then the pairs would have been 2,5 or 3,4. 2,5 are again multiplications of prime numbers which have been removed, so the only possibility (in retrospect again) is that the pair was 3,4.

1 < x < y then the only possible solution (using set theory) is that the pair is 3,4 and that the sum was 7 product was 12.

As long as neither of the two people have lied, or made any mistakes, then it seems that 3,4 is the only option:

3,4 (giving the Dilemma for the Sum as being 7 - either 2,5 or 3,4 - when he finds out the product does not give the solution, he knows its not 2,5 and :. 3,4).


3,4 product 12 - for which he has two answers -2,6 or 3,4. He knows that if the answer was 2,6 then the sum would have been 8, for which the sum guy has 3 possible choices, so thats not solvable), forcing him to select the 3,4 option.


Did I miss something from my summation of the rules? (if there was a rule which said 1 < x < y then it also adds more sets of answers into this set)

Also, I think I have the same solution as the last guy to post. but different workings out.

[jejt]

The solutions which match the additionl rule

1 < x < y

actually are where sum = 7 or 8 Having the sum as 7 was discussed in my previous post, but having the sum of 8 was not.

If this rule is in place, therea are two possiblities: 2/5 and 3/4. Because 2 and 5 are primes, their product (10) is only atainable by 2*5, so the product would have lead straight to their solution. There is no other dilemma solution for the Sum.

There are of course potentially other solutions involving simultatious solutions, but 7 is still the smallest.

[mspeed]

Big K,
if all d engineers in this forum r giving it there best shot and u still haven't gotten an answer or probably waving it because of inappropriate deductions, then i can say, the question is about teamwork if both Ash and Maro talk about what they know about the question then an answer would arise.

secondly,if u told us the numbers u gave them we can come up wit something.

[ishak.hussainul]

Originally Posted by gravz84

it is indeed the first product which satisfies but there are others that have 2 possibilities that are solved by Ash only after the 1st 2 statements are made.
So in my opinion there are many such solutions but 3,4 is the least one.

i also thout the same.
but it is not correct....
more than 2 possibilities may occur.
but only one possibility must be confusing..i mean all other possibility may give the one (who knows the product) the correct answer.....

[nishank_eureka]

This is a very tricky question. I think some programming is required. I will post the programme as soon as i am done. Logic will be pretty much clear from the programme itself.