hmmm...seems like a hard one -____-

Two perfect logicians, S and P, are told that integers x and y have been chosen such that 1

Question

hmmm...seems like a hard one -____-

Two perfect logicians, S and P, are told that integers x and y have been chosen such that 1 < x < y and x+y < 100.  S is given the value x+y and P is given the value xy.  They then have the following conversation.

P:  I cannot determine the two numbers.
S:  I knew that.
P:  Now I can determine them.
S:  So can I.

Given that the above statements are true, what are the two numbers?

lgbasallote · Answer

...i dont know what you mean o.O haha

callisto · Answer

x=4, y=6?

lgbasallote · Answer

hmmm close...but not quite :P hehe

callisto · Answer

x=6, y=7? (seems i'm gonna guess all numbers lol)

anonymous · Answer

x<10?

anonymous · Answer

9and 10?

lgbasallote · Answer

still no callisto :P wrong aron :p

mani_jha · Answer

Lol..I don't think the conversation gives us any hint about what the numbers are -_-. They could be anything more than 1(and with a sum less than 100)!

callisto · Answer

Nope.. I cannot determine the two numbers <-- either x or y is a prime, or neither of them are prime. If x and y are both prime, p would know immediately..

lgbasallote · Answer

hmmm or maybe they\re hints -____-

anonymous · Answer

4,13?

anonymous · Answer

only P and S knows the answer...

lgbasallote · Answer

which is x..which is y @CoCoTsoi

anonymous · Answer

x=4,y=13

callisto · Answer

=.= lgba ....1<x<y

lgbasallote · Answer

nice!!! howd you get it @CoCoTsoi ? @Callisto what about it??

anonymous · Answer

yeah! I explain it now.:D

anonymous · Answer

http://www.qbyte.org/puzzles/p003s.html

anonymous · Answer

googled, though i dont like it :/

anonymous · Answer

I did not search it from Google :)

anonymous · Answer

i haven't told u that u searched it from google :)

lgbasallote · Answer

why not like it arnab??

anonymous · Answer

because it can't distinguish a good problem solver and a bad one, i think..

lgbasallote · Answer

oh..hmmm guess not =))) but it is a riddle so it relies on logic not problem solving hehe

anonymous · Answer

From 1 < x < y ,
we can now x and y are different. 
i.e. xy will not be 4,9,16,25,......

From P:  I cannot determine the two numbers.,
xy cannot be 3,5,7,11,.......

From S:  I knew that.,
x+y has more than 2 factor other than 1 and itself
Therefore, x+y cannot be 6,8,15,......

From P:  Now I can determine them.,
sum of the factors cannot equal to the sum of factors of the other numbers. 
e.g. 4+8, 2+10
Therefore, xy is not 20,12,......

The only number left is 52 which is 4x13

I list 2-100 on the paper. Then I write down their factors. After that, I cancel the impossible numbers. Finally, I got 52.

It is quite time-consuming XD

lgbasallote · Answer

AMAZING!!!!