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

I'm assuming it's something to do with their only being one possible combination of numbers that add together to make something that you can't use to find the product of the two numbers?

If that makes any sense...
 
Now, the interesting bit is where Simon says "I know you don't know". As said in the OP, any even number is the sum of two primes. If the sum (which Simon knows) were even, then there was the possibility that both x and y were prime, meaning Peter would certainly have known the answer immediately. Since Simon knew there was no chance of this, we can infer that x + y is odd. Therefore we're looking at one even number x and one odd number y.

So x+y is odd.
x*y is even.

That's as far as I've got so far.
 
I don't believe, for one second, that any of the people who claimed to arrive at the solution to this problem actually did so by any other means than google (it's a very famous problem).
 
w11tho said:
I don't believe, for one second, that any of the people who claimed to arrive at the solution to this problem actually did so by any other means than google (it's a very famous problem).
Click to expand...

Exactly, and many people have already done it before. I knew the answer, and I know people will call google.

Fair enough.
 
Didn't realise that it was such a famous problem, only heard of it today


To anyone who's posted the answers: please could you edit your post so that anyone else who wants to figure out the answers can do so and read the thread at the same time?

Thanks :)
 
SlyReaper said:
Now, the interesting bit is where Simon says "I know you don't know". As said in the OP, any even number is the sum of two primes. If the sum (which Simon knows) were even, then there was the possibility that both x and y were prime, meaning Peter would certainly have known the answer immediately. Since Simon knew there was no chance of this, we can infer that x + y is odd. Therefore we're looking at one even number x and one odd number y.

So x+y is odd.
x*y is even.

That's as far as I've got so far.
Click to expand...

Continued:

So the only new information Peter has is that x is odd and y is even, and somehow is able to deduce what they are simply by knowing the product. Therefore there was previously the possibility that the product was actually the product of two even numbers, and that, now that possibility is eliminated, only one possibility remains.

So peter has a number that can be factorised in exactly two ways: one into even and even, one into odd and even. From the fact that it could have been even*even, the product must be a multiple of 4. Since there is only one factorisation remaining, the odd number must be prime.

So by dividing by 4, Peter gets his odd number. Now Simon can follow the same line of reasoning when Peter declares he knows what the two numbers are (the two numbers being 4 and [some prime]). So all he has to do is subtract 4 from his number to get his answer.
 
SlyReaper said:
Now, the interesting bit is where Simon says "I know you don't know". As said in the OP, any even number is the sum of two primes. If the sum (which Simon knows) were even, then there was the possibility that both x and y were prime, meaning Peter would certainly have known the answer immediately. Since Simon knew there was no chance of this, we can infer that x + y is odd. Therefore we're looking at one even number x and one odd number y.

So x+y is odd.
x*y is even.

That's as far as I've got so far.
Click to expand...

What if x = 2 and y = 3? Then both of your criteria are satisfied, and yet Peter can immediately deduce from his product 6 that the two numbers must be 2 and 3.
 
Inquisitor said:
What if x = 2 and y = 3? Then both of your criteria are satisfied, and yet Peter can immediately deduce from his product 6 that the two numbers must be 2 and 3.
Click to expand...

Some odd numbers are also the sum of two primes, and 5 is one of them. Simon has the sum, so if the sum were 5, he wouldn't say "I know you don't know".
 
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