simple math question for realm 2 -closed- congrats Lman360-
Moderator: moderators
-
Guest
It's not really important HOW they move on the cube. Just whether the exact opposite point of the cube is the longest path along the surface.Canadian Energy Corp. wrote:I think its better if the fly starts in the top/bottom corner on the same side of the spider. I am not sure, but that sounds right.
The solution goes something like this:
If we say the side of the cube is 1 and the spider sits at the middle of one of the edges, then the shortest path to the middle of the opposite edge of the cube has the length 2. Now, if that spider would move a short distance 's' from the middle, then the shortest length from the spider's location is:
min [SQRT(4+s
Last edited by Guest on 07.05.2008, 20:14, edited 1 time in total.
-
Guest
I can do this one with induction but I'm a math major and I'm tired of math lol (that's really my excuse for not being able to do the other problems =p). The basic idea (for those who don't know) is that if you can assume there's a non-constant polynomial where f(n) has x prime factors, then if you can prove it for m, n<m where f(m) has x+1 distinct prime factors then it's true for any x. All in all, not a fun process lolNordic Group wrote:
Let f(x) be a non-constant polynomial with integer coefficients. Prove that there is an integer n such that f(n) has at least 2004 distinct prime factors.
If you want an answer for n, multiply out f: (x-1)(x-2)(x-3)(x-5)(x-7)....until you have 2004 products of prime factors. I'm guessing that's where programming comes in.
-
Guest
-
Guest
Well the induction step would be quite difficult to prove, I imagine.
It's a number theory problem, so one solution that I know of uses the Chinese Remainder theorem, but it's way too difficult for me to understand. I hate number theory!! The other solution is a lot more mind-friendly. Basically you are trying to prove the opposite, and assume there is an integer m, so that f(m) has the highest number of prime factors. We can also assume, that m=0, so if you take that f(0)=k, then for every w f(wk
It's a number theory problem, so one solution that I know of uses the Chinese Remainder theorem, but it's way too difficult for me to understand. I hate number theory!! The other solution is a lot more mind-friendly. Basically you are trying to prove the opposite, and assume there is an integer m, so that f(m) has the highest number of prime factors. We can also assume, that m=0, so if you take that f(0)=k, then for every w f(wk
-
Guest
I have a strong feeling I proved a problem very similar to that when I took my number theory course because the Chinese Remainder theorem sounds very familiar. If I ever get bored I'll go back through my notes.
For someone too young for a university you've got a brilliant math mind. If you can learn programming with it, there are a ton of things you can do, especially in the field of cryptology.
For someone too young for a university you've got a brilliant math mind. If you can learn programming with it, there are a ton of things you can do, especially in the field of cryptology.
-
Guest
wouldnt it be easyer if the spider went to the fly so the fly dosnt move at allCanadian Energy Corp. wrote:Nordic Group wrote:
And finally a fairly easy one:
A spider and a fly are sitting on a cube. The fly wants to maximize the shortest path to the spider
along the surface of the cube. Is it necessarily best for the fly to be at the point opposite to the spider?
("Opposite" means "symmetric with respect to the center of the cube".)
