The Flying Gorilla Problem

[Ender]

I never accused you of saying it was  ;)

[Sidoh]

Your reply sure made it sound like you were. :P

[dark_drake]

Your reply sure made it sound like you were. :P

just never spend so much time on the semantics of a problem.

The problem doesn't make any sense in the way that I (correctly, I may add :P) interpreted it.

In any case, though, these sorts of problems are widely viewed as a waste of time.  You may get the occasional answer, but unless you're posting something that's seemingly more profound, then don't expect to get many replies.  It's not that people here aren't capable of solving these sorts of questions. :p

I am unaware of any formal mathematical notation where a comma suggests what you're saying this did.  If you're going to post riddles from elsewhere, at least clean up the garbage. :P

0 < s, t < 1

It's all in the first quadrant.

Is this what you were intending?  It seems to me that there are an infinite amount of (real) solutions in both the first and fourth quadrants. :P

Aside from that, I don't see how the way numbers fall into quadrants relate to your choice of sets for this problem. :P

has an infinite amount of negative components.

Do you mean ordered pair of numbers (s, t) in the set ? :P

COUNT THE TONGUE SMILEYS!!! JUST COUNT THEM!!!! THEY ARE STARTING TO BURN MY EYES I SEE THEM SO OFTEN!

Edit: Zeus told me 4 answers if 0,0 isn't a possibilty.

[Ender]

Solution:

The shape from which we will count the lattice points has four vertices. Each vertice is a solution of the ordered pair (3s + 7t, 5s + t) with (s,t) as (0, 0), (0, 1), (1, 0), (1, 1), since these represent the bounds of s and t: 0 < s < 1 and 0 < t < 1. There are 31 lattice points, and thus 31 solutions.

Draw it out and it will make more sense.

[dark_drake]

Solution:

The shape from which we will count the lattice points has four vertices. Each vertice is a solution of (3s + 7t, 5s + t) with (s,t) as (0, 0), (0, 1), (1, 0), (1, 1), since these represent the bounds of s and t: 0 < s < 1 and 0 < t < 1. There are 31 lattice points, and thus 31 solutions.

Draw it out and it will make more sense.

so that's actually a greater/lesser than or equal to sign?

[Sidoh]

so that's actually a greater/lesser than or equal to sign?

() indicates an open interval (all points between the components, but not including the components).  [] indicates a closed interval, including all points between the components as well as the components.

IE, a domain of (0,10) would indicate 0 < x < 10.  A domain of [0,10] would indicate 0 <= x <= 10.

[dark_drake]

() indicates an open interval (all points between the components, but not including the components).  [] indicates a closed interval, including all points between the components as well as the components.

IE, a domain of (0,10) would indicate 0 < x < 10.  A domain of [0,10] would indicate 0 <= x <= 10.

Interval notation is lame; I know it, but I just prefer the symbols.

[Sidoh]

Interval notation is lame; I know it, but I just prefer the symbols.

Lazy shorthand becomes perfered after you work for an extended period of time on the subject.

[Ender]

Yes, notation can be daunting but it makes math much easier to communicate.