Math Puzzle

[Hacp]

So is Obama the only one brave enough to offer a solution?

 

[JJChicken]

This line is incorrect
Actually when X=666, 2A*Y/X = 2Y.

Spot on!

 

[Mike Gayner]

Hmm are you willing to put money on it? My friend is right next to me and he assured me that it wasn't infinite. He's willing to put 10 bucks on the line.

I know I'm right but I don't want his $10. Eventually US currency is going to be worth zero, and I don't want money I can't use.

 

[GodlessAstronomer]

So is Obama the only one brave enough to offer a solution?

I'm working on one I'm not great at discrete maths so I'm pessimistic about getting the first answer. Props to the pres for trying

 

[Adrenaline]

So a friend presented me with this little math puzzle. It seems like a tricky beast. Given 335x+666y=K where X, Y, and K are positive integers, what is the largest K that can not be formed . It seems a little tricky, but there must be an easy way to get the answer. He told me it had something to do with 1001. That was the only hint he gave me. I might write a program to check it out but in the meantime some of you math-magicians might already know the answer.

My guess from this weird worded math problem:

The number 0 is an integer but is not positive, as the problem states is required. If x and y were 0 then k would be 0, but this can not be done.

Now, if x and y were 1 then k would be 1001 according to the equation. The largest K, an integer, that could not be formed would be 1000.

 

[GodlessAstronomer]

Now, if x and y were 1 then k would be 1001 according to the equation. The largest K, an integer, that could not be formed would be 1000.

What about 1002?

 

[Adrenaline]

What about 1002?

I thought about that, you could make the case for k-1 at any point for x and y. But if you were to make a line with the smallest possible integers available then it would be 1001-1. 1000 is the largest number that cannot be formed.

I guess. Like I said, it is worded weird to me.

 

[GodlessAstronomer]

I thought about that, you could make the case for k-1 at any point for x and y. But if you were to make a line with the smallest possible integers available then it would be 1001-1. 1000 is the largest number that cannot be formed.

I guess. Like I said, it is worded weird to me.

No, there will be a point at which ∀(K(x,y) > Z) ∃(K(x1,y1) : K(x1, y1) - K(x,y) = 1) and the answer to the problem is Z-1.
Or I assume that this is that case, otherwise the OP is just messing with us. It makes intuitive sense to me that this is the case because 335 and 666 are coprime, but I don't know how to prove it.

 

[Adrenaline]

No, there will be a point at which ∀(K(x,y) > Z) ∃(K(x1,y1) : K(x1, y1) - K(x,y) = 1) and the answer to the problem is Z-1.
Or I assume that this is that case, otherwise the OP is just messing with us. It makes intuitive sense to me that this is the case because 335 and 666 are coprime, but I don't know how to prove it.

I do not recall any of those weird math symbols in any class I took in college (Cal I, II, III, DE and LA). I am going off simplicity here. No matter what positive number of a slope you would choose the largest integer k could not be would be 1000.

Then again, it is worded weird to me.

 

[GodlessAstronomer]

This is discrete maths so thinking about slopes can get you into trouble. The upside-down A is "for all", the backwards E is "there exists some" and the colon means "such that", so that notation reads:
For all K(x,y) > Z there exists some K(x1,y1) such that K(x1,y1)-K(x,y) = 1

 

[GodlessAstronomer]

Damn OP is no longer online. Hacp when you get back, is the answer 56944?

 

[Adrenaline]

This is discrete maths so thinking about slopes can get you into trouble. The upside-down A is "for all", the backwards E is "there exists some" and the colon means "such that", so that notation reads:
For all K(x,y) > Z there exists some K(x1,y1) such that K(x1,y1)-K(x,y) = 1

Yeah, well ummmm, have fun with that.

 

[JJChicken]

No, there will be a point at which ∀(K(x,y) > Z) ∃(K(x1,y1) : K(x1, y1) - K(x,y) = 1) and the answer to the problem is Z-1.
Or I assume that this is that case, otherwise the OP is just messing with us. It makes intuitive sense to me that this is the case because 335 and 666 are coprime, but I don't know how to prove it.

Hey how did you do those symbols (plus any others)? I'm trying to create a math website and this would be very helpful.

 

[JJChicken]

Damn OP is no longer online. Hacp when you get back, is the answer 56944?

How did you get that number? I can follow your logic in the above post, but dunno anything about discrete maths (or not much yet - going to do a masters in a year or two in quantitative finance so will learn alot of this stuff then).

 

[GodlessAstronomer]

Hey how did you do those symbols (plus any others)? I'm trying to create a math website and this would be very helpful.

Just got them from here http://en.wikipedia.org/wiki/Table_of_mathematical_symbols

How did you get that number? I can follow your logic in the above post, but dunno anything about discrete maths (or not much yet - going to do a masters in a year or two in quantitative finance so will learn alot of this stuff then).

I've since discovered that number is wrong, so never mind

 

[GodlessAstronomer]

I have an answer but I don't know if it's right. My number is K = 224,099.

Will post my solution soon, it's slightly complicated and it's past midnight here.

Edit - shit wrong again. How depressing

 

[DrPizza]

Pretty simple & common problem from discrete mathematics.

 

[jersiq]

I am still failing to see how it isn't Diophantine, and since GCD(335,666)= 1, we have infinitely many solutions.

Edit:

Yeah, I am sticking to it.

Since GCD(335,666) = 1 we can rewrite as an integer linear combination:

167*335 + (-84)*666 = 1

Since there is one solution there are infinitely many. Proof: Theorem 1.4.4 found here: http://www.usna.edu/Users/math/wdj/book/node13.html or any common number theory book.

EDIT: X2..... Waaayyyyy off the reservation on this one. I guess math before coffee = fail in my house.

 

[Hacp]

I have an answer but I don't know if it's right. My number is K = 224,099.

Will post my solution soon, it's slightly complicated and it's past midnight here.

Edit - shit wrong again. How depressing

He said its wrong. Now that you've all given up, he told me its the Frobenius Problem.

 

[Fenixgoon]

Pretty simple & common problem from discrete mathematics.

care to explain?

isn't the equation just a plane in space, and extends infinitely?

 

[Crusty]

care to explain?

isn't the equation just a plane in space, and extends infinitely?

Discrete math. The OP set constraints that X and Y were positive integers so the only possible outcome of the equation is yet another positive integer, not every possible value that lies on the plane defined by the equation.

 

[silverpig]

The trick is proving that you can find some integer Z such that you can make every integer above Z with some combination of 335 and 666.

Without doing any work, the answer is probably something simple like 335*666-1 = 223109

 

[Adrenaline]

The sad thing is I looked up Frobenius Problem on wikipedia and the concept seems simple. Following their chicken nugget example made the concept easy. Have fun finding the number.

 

[TuxDave]

aw crap. Apparantly I screwed up the smallest values to increment the value by one. But once you get one of:

167*335 + (-84)*666 = 1

And another of
666*x-335*y = 1

Then if you have 83*666 and (y-1)*335, you can't increment by one so the answer is that +1?

 

[canis]

So a friend presented me with this little math puzzle. It seems like a tricky beast. Given 335x+666y=K where X, Y, and K are positive integers, what is the largest K that can not be formed . It seems a little tricky, but there must be an easy way to get the answer. He told me it had something to do with 1001. That was the only hint he gave me. I might write a program to check it out but in the meantime some of you math-magicians might already know the answer.

Total crap reproduction of the original problem. For this problem there is no upper bound to K. For the original problem, the answer is 222109.