Hard maths problem for you (Warning: VERY hard!)

TheCenturion

TheCenturion

TheCenturion

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18 Mar 2008
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This is genuinely hard, I would be very surprised and imrpressed by a member who could get the correct answer and doesn't have any maths qualifications above A level!

I can't quite remember it correctly, I think that this is how it goes. If I write it wrong, I'll edit it and tell you :)

A mysterious stranger (paedo bear maybe?) talks to Sam and Paul. He thinks of two integers between 2 and 99 inclusive. He tells Paul the product of the two numbers, and tells Sam the sum of the two numbers. Paul and Sam then talk to each other, without saying the number that they've been told. They do however, know the nature of the number that the other's been given (ie: Paul knows Sam's been given the sum of the two numbers and visa versa)
Paul: I don't know what the two numbers are.
Sam: I know you don't know, neither do I.
Paul: AHA! I know what the numbers are now!
Sam: Ah, so do I


I'm not sure where to start. I know that there's a piece of mathematics that might be useful in this case: it's a rule that states that any given even number greater than 2 can be made by adding two prime numbers together.

Oh and: if you happen to figure it out, please don't spoil it for the rest of us, not to begin with at least ;)

98C2= 4753 number of possible number combinations, so trial and error probably won't work for this :p
 
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Peter: I don't know what the two numbers are.
Simon: I know you don't know, neither do I.

* Peter takes out a pen and writes his number on his hand, as does Simon *

Peter: AHA! I know what the numbers are now!
Simon: Ah, so do I
 
Garee said:
Peter: I don't know what the two numbers are.
Simon: I know you don't know, neither do I.

* Peter takes out a pen and writes his number on his hand, as does Simon *

Peter: AHA! I know what the numbers are now!
Simon: Ah, so do I
Click to expand...


I see you've used an exceptional amount of maths knowledge to reach that answer :D
 
I'm pretty sure I would have just stabbed the mysterious stranger in the eye with a pencil and not have to go through all that hassle.
 
Not able to solve it without much more work and thinking - might not be able to solve it even with hard work. Still a couple of things stand out.

Looking at Peter's information the number isn't going to be the product of two primes else he would know the two numbers.

Looking at Simon's information one number must be even and the other odd - making an odd number. One of our lecturers taught us about a conjecture that every even number can be written as a sum of primes. So if Simon knows Peter doesn't know then the number must be odd.

That makes sense I think. Taking it on further I guess from what Peter says he must be using the fact that the sum is odd.

Interesting problem - not too sure how to progress.
 
They could be any numbers based on what information you've given, if you said the sum = product or something then...

or maybe I'm just blind.

EDIT: Oh wait I'm starting to get it now...
 
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