It’s a mathstorm

Well it’s been a long time since I’ve had any real time to do much posting here.  The senior design course I’m in is sucking up a large proportion of my time.  I don’t see this changing any time soon, either.

Anyway, as of Monday, we were assigned projects in the Number Theory class I’m taking.  I chose to solve a “difficult” problem.  It goes like this:

An alien appears to two mathematicians, Sam and Polly. The alien says, “I’m thinking of two numbers X and Y with 3 ≤ X ≤ Y ≤ 97. I will tell their sum to Sam and their product to Polly.” The alien does this and then disappears. The following conversation occurs:
Sam: You don’t know what X and Y are.
Polly: That’s true, but now I do.
Sam: And now I do too.
Find X and Y.

So far I’ve managed to narrow down the possibilities to some 280 pairs.  I haven’t yet accounted for all the information present, though.

6 Responses to “It’s a mathstorm”

  1. Ooh… I remember doing similar problems in JHschool, of course much simpler, but the general idea is the same.

    Maybe I should take Number Theory when I get older…

    Now you have me obsessed with solving this one. Are you going to post the answer when you get it?

  2. Yourself says:

    I have the answer. I’ve had it for quite a while, actually.

  3. “I have the answer. I’ve had it for quite a while, actually.”

    That’s good, considering it was assigned a while ago. :)

    What is it? I understand the problem itself, but I’ve only been able to eliminate most combinations which are both even or both odd. (ending up with an even sum, which most of which could be written as the sum of two primes, so Sam couldn’t know that Polly couldn’t possibly know)

    I tried to continue eliminating pairs, but the rest is way over my head.

  4. Yourself says:

    “That’s good, considering it was assigned a while ago.”

    It’s not due yet.

    “(ending up with an even sum, which most of which could be written as the sum of two primes, so Sam couldn’t know that Polly couldn’t possibly know)”

    Excellent observation. This is really the key observation you need to make. Nothing more advanced (mathematically) is required.

    “What is it?”

    I’m not telling.

  5. “It’s not due yet.”
    Oh.

    “Excellent observation. This is really the key observation you need to make. Nothing more advanced (mathematically) is required.”

    “I’m not telling.”

    Okay, I’ll keep at it.

  6. Falk Flyer says:

    …uh…now can you tell us? I’ve been trying to figure it out for a while, but I can’t even get to the whole “eliminate pairs” step. 0.o