Thread: Geniuses

2 geniuses, A and B were given a problem.They were told that integers x and y have been chosen such that 1 < x < y and x+y < 100. A is given the value x+y and B is given the value xy. They then have the following conversation.

B: I cannot determine the two numbers.
A: I knew that.
B: Now I can determine them.
A: So can I.

what are the two numbers?

A is been given the sum and B is given the product.
They are not allowed to disclose these.
Like if sum = 16
then x and y can have many possibilites!!

hi smart coder,

so your solution have only one combination to satisfy the conditions..

1<x<y<100 and x+y < 100....

interesting...i can't find the answer....waiting for someone reply....

----------------------
suresh

Hey Smart Coder i'm getting as 3,2

X=3
Y=2

X+Y = 5
X*Y = 6

Which satisfies all the condition. But the doubt here X+Y is more than enough to predict the answer.

The only thing i found out is X*Y cannot be prime and also its square...

Thanks
Manoj

Answer is wrong Manoj

Tell me which part is wrong in my answer, so that i can correct it...

Thanks
Manoj

u hvent told ne part of ur solution...u hvent told how u used the statements of the geniuses!!
explain ur solution in detail and tell wt u deduce after every statement!!

hi smart coder,

any clue for finding the answer ?

---------------
suresh

xy cannot be a prime or any power of prime!!

hi smart coder,

"B: I cannot determine the two numbers.".
What it means the above statement ? B already know the value of xy and x+y. but he doesn't know the value of x and y. Is it correct ?

Or

he know only the value of x+y. i am confusing here..that's why i ask give some clue...but whatever you told already manoj mentioned that one..

sum of x+y is more than 7 then there should be two more combination will come. For example if the sum is 8 then (x=2,y=6) and (x=3,y=5). But you told only one combination will comes here...

-------------------
suresh

A is only given the value of x+y and B is only given the value of xy.
Look the problem is too too tough, it took me a time to understand the whole solution. There is a lot of calculation involved in this question. If u people agree then I wud give the solution!!

Here is the answer,

X=4 and Y =13

x +y =17 and xy=52

Is that right Smark Coder?

Solution is available here...
http://www.qbyte.org/puzzles/p003s.html