Two numbers and two logicians

[wheeler]

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But both m and n are >1.

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Thank you. I'm an idiot. I screwed up and solved the 1 <= m < n problem, which surpising also has a unique answer!

[durron597]

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Answer: <font color="white">1 and 16</font>

I can't believe no one got it already. (I must admit I used Mathematica to do the tedious bits.)

Edit: neat puzzle!

[/ QUOTE ]

Um, I got it, and my answer is correct unlike yours.

Sirio got it before me except he didn't post the solution, just the answer.

[TomCollins]

T1: I cannot determine the two numbers- He can only deduce his number is not the multiple of two primes.
G1: I already knew that- He knows that his number cannot be the sum of two primes.

Now the tedious parts.

[PairTheBoard]

[ QUOTE ]
[ QUOTE ]
Answer: <font color="white">1 and 16</font>

I can't believe no one got it already. (I must admit I used Mathematica to do the tedious bits.)

Edit: neat puzzle!

[/ QUOTE ]

Um, I got it, and my answer is correct unlike yours.

Sirio got it before me except he didn't post the solution, just the answer.

[/ QUOTE ]

I got it, and I think my proof is easy to follow.

PairTheBoard

[kyro]

I spent a lot of time on this one. I'm patting myself on the back now.

[durron597]

[ QUOTE ]

I got it, and I think my proof is easy to follow.

PairTheBoard

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I'm a douche [img]/images/graemlins/wink.gif[/img]

[wmspringer]

<font color="white"> Hmm.

Since T cannot determine m and n, mn must be some number with more than 2 distinct factors other than itself and 1 (as 1 is not allowed and n,m are different)

Since G knew T couldn't determine m,n, n+m must have no two distinct prime numbers that add up to get it. (Every composite number is the sum of primes, but not necessarily of two distinct primes)

After the first two statements, T takes every set of two numbers that multiply to get mn, removes those that add up to a number which is the product of two primes, and has one possibility left.

After the third statement, G knows that T was able to do that, so he can find the numbers as well.

But I'm not gonna go through all the integers up to 100 to figure out which ones it was :-p
</font>

[wmspringer]

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<font color="white">Just started thinking here. I think it has something to do with n being a negative integer. No n is 0 maybe. Gotta think on this. </font>

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<font color="white"> You forget that it's given that m and n are both greater than 1 </font>

[lgas]

I think the answer is: <font color="white">2 and 15</font>