There's an interesting math puzzle, posted first in ![[info]](http://l-stat.livejournal.com/img/community.gif){kind=small}
ucberkeley
and then reposted in ![[info]](http://l-stat.livejournal.com/img/userinfo.gif){kind=small}
nibot_lab. A variant also appears on
a puzzle page.
I think I can solve this (kind) of problem using a Python program. But my question to you, smart people, is
can you solve it using just pen and paper? (I can't.)
Two numbers are selected from the set of integers from 3 to 98, inclusive. A woman is told the product of the numbers; a man is told their sum. The man and the woman have the following conversation:
Woman: I don't know what the numbers are.
Man: I know that already, but I don't know the numbers either.
Woman: In that case, I know what the numbers are.
Man: So do I.What are the numbers?
(I removed the requirement that the numbers be distinct from the original formulation since I believe this leads to no solution.)
Comments
And is there any reason to believe that we can figure out this puzzle? Could there be multiple sets of numbers meeting this criteria?
I guess I was hoping that since it was posed as a puzzle in a couple of fora, there is a clear way to answer it. Then again, like I said, I believe the original formulation has no solution, so perhaps not.
-Ogre
I've got a comprehensive analysis/solution to this (and the [2,100] variation) mostly written up, I'll post it when I have a chance. In any case, while you can get really far with the logic, I don't think there's an elegant way to solve it on pen and paper alone, as verifying which numbers satisfy the third and fourth statements requires an inconvenient number of computations (for a person. It takes no time in matlab.)
Arglebargle.
This is such a fun puzzle =)