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Math Puzzle

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Hacp

Hacp

Lifer
Jun 8, 2005
13,923
2
81
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.
 
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dighn

Lifer
Aug 12, 2001
22,820
4
81
I should be sleeing but I don't understand what is meant by "what is the largest K that can not be formed". There's no upper bound on values of k that have no solutions - it just needs to be something not divisible by 333.

edit: ahh you edited your question
 
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GodlessAstronomer

GodlessAstronomer

Lifer
Oct 27, 2007
17,009
5
0
Edit - just to clarify the first few posts in this thread, the OP accidentally gave us the numbers 333 and 666 to begin with.

dighn said:
I should be sleeing but I don't understand what is meant by "what is the largest K that can not be formed". There's no upper bound on values of k that have no solutions - it just needs to be something not divisible by 333.
Click to expand...
This is my thinking, I'm guessing he wrote the question wrong.
 
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E

eLiu

Diamond Member
Jun 4, 2001
6,407
1
0
dighn said:
I should be sleeing but I don't understand what is meant by "what is the largest K that can not be formed". There's no upper bound on values of k that have no solutions - it just needs to be something not divisible by 333.
Click to expand...

er, x and y are positive. So if x>=1 and y>=1, the smallest number you can form is 999.

So i guess the answer is 998?

But this wasn't much of a puzzle. I'd vote with "question is not stated correctly" too.
 
GodlessAstronomer

GodlessAstronomer

Lifer
Oct 27, 2007
17,009
5
0
eLiu said:
er, x and y are positive. So if x>=1 and y>=1, the smallest number you can form is 999.

So i guess the answer is 998?

But this wasn't much of a puzzle. I'd vote with "question is not stated correctly" too.
Click to expand...
The problem asked for the largest value K could not achieve. The given equation can't be solved for, say, K=1000, which is bigger than 998.
 
J

JJChicken

Diamond Member
Apr 9, 2007
6,165
16
81
I AM SUCH A FOOL. THE BELOW ANSWER IS WRONG :( :


The question asks the largest K that cannot be formed. K's equation shows that K's maximum value is not limited in any way. The set of K numbers is countably infinite.

We must approach this question differently. We want to establish the situation where every unit increase in X or Y will create a unit increase in K. For sake of clarity, lets call the K at this point "K1". After such a point, all possible integers after "K1" can be produced by the formula for K.

Let A = 333X

Thus, 666Y = 2A*Y/X and our equation for K can be re-written as

K = A + 2A*Y/X.

The function A increases in discrete steps of 333 for each unit increase in X. This does not help our cause so ignore it.

We want to find the situation where 2A * Y/X can increase by 1 for every unit increase in X or Y.

The answer is when X = 2*333 = 666. Because at this value, 2A * Y/X is = Y. And every unit increase in Y (holding X constant at 666) will cause a 1 unit increase in K.

The K (K1) value at this point is 333*333*2 + 666 = 222,444

Thus, the largest K that cannot be formed is 222,443.
 
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Hacp

Hacp

Lifer
Jun 8, 2005
13,923
2
81
Ok I asked my friend again and it is 666x+335y=k and the 999 is 1001. I am wondering if it is an actual problem now since he keeps changing the answers. It seems he is coming up with this stuff from his ass.
 
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