Thread: Logic problem

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? (computer assistance is allowed.)



Moderator edit: Apporved Challenge question.

Originally Posted by wonderboy1953

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? (computer assistance is allowed.)



Moderator edit: Apporved Challenge question.

P: I cannot determine the two numbers. - the number I have is not the product of two primes

S: I knew that. - the sum I have cannot be the sum of two primes

P: Now I can determine them. - there is only one factorisation such that the sum cannot be the sum of two primes

S: So can I. - there is only one decomposition of my number into a sum such that the sum of a factorisation of their product cannot be the sum of two primes

CB

Quite a golden oldie:

Google

Originally Posted by Wilmer

Quite a golden oldie:

Google

I am reasonably sure that I have solved this (or a number of problems remarkably like this) before as a NewScientist Enigma.

CB

13 and 4

Originally Posted by MSM

13 and 4

You're the winner (good job).

Originally Posted by Wilmer

Quite a golden oldie:

Google

An oldie but goodie (honestly I do try to post in stuff that's either hard to find or fresh).