The Fucking Goat Problem

The fucking Goat Problem, or how to make a bunch of young people feel like idiots.

Now, a trauma from my school years.

No, it doesn’t involve goats, and it doesn’t involve fucking! I’m no fucking hillbilly! No goat fucking!

However, the question at hand involves goats and farmers and circular pastures and shit all…

Ok, moving on.

The Fucking Goat Problem

How do you make young people feel like idiots?

You throw the fucking Goat Problem at them. (No, not the Goat Fucking Problem, that’s another problem involving a couple of other farmers… and possibly a Dutch racist or two…)

This problem can be summarized as:

Two farmers share a circular pasture. One farmer can tie a goat at one of the poles in the fence around the pasture to allow his goat to graze it.

How long should the rope be to allow the goat to graze only half the area of the pasture?

You might think, easy peasy! It’s a circle and a radius and shit. I know this.

Well, you’d be wrong. Because it’s a circle bisected by another circle and wee hoo… the solution to this ought to shut you up for about half of the rest of your life.

This one calculates the area. Now all you have to do is find r or R or d or what-fucking-ever. Yeah, right.

Formula for the area of two bisecting circles

Reality Check

Ok. Time for a reality check.

Circular pasture? Really?

Obviously, this is either some form of insult to farmers or someone has been in a place where they don’t know how to set up pastures!

I think the moron that came up with the question should be asked to calculate the area between the circular pastures… given that the total land containing pastures in the village where the farmers live is shaped like an upside down Prince symbol! (Yeah, that totally looks like a dick with a really scary piercing and funky pubes…)

Next.

So, one farmer gets to let his goat graze the pasture until it has eaten all the grass and only then can the other farmer let his goat graze the rest?

Or are we suggesting the other goat should be tied with a rope that contracts and expands to keep it off the area the first goat can graze? (I think that’s how the west deals with the third world, right?)

I’m not a country bumpkin, by any means, but even I know a goat might take weeks to graze a whole pasture, maybe even the whole summer.

But both goats have to eat at the same time or the other fucking goat will be dead long before the first one is done!

Fucking goat killing!

We don’t do that… part from when we totally do that to eat the fucker… or maybe… goat cheese? Possibly… Goat milk? Yech! Goat pie? Fuck no!

Ok. We don’t kill goats!

Maybe we should just put a fence in the middle of the pasture? Or?

Sorry. I know. That would totally remove all the brain torture qualities of the question.

Reality check, part 2: Real Goat Farmers

Here’s what a real goat farmer would do once he’s spent all his money building a worthless circular pasture so he can’t afford a fence along the middle:

Tie each goat at opposite ends of the pasture with ropes that makes it possible for the goats to graze all the way to the middle of the pasture.

Then he would pray the fucking goat doesn’t bite off the rope… maybe a chain instead?

When the grass has been grazed, move the ropes 90 degrees along the fence in the same direction, placing the goats once again at the opposite side of one another, and allow them to graze the rest of the pasture.

No, I’m not going to draw you a fucking picture!

And besides. Goat farmer? I thought they were goat herders! But, sure, that’s the least surreal thing about the whole question.

Reality check, part 3

Did you really buy all that crap about ropes/chains and moving around and shit?

Do you want to know what two really real goat farmers/herders would do if they, by some bizarre circumstance ended up with a circular pasture that had to be shared by two goats?

Can you guess?

Really? No?

They would put the two fucking goats in the fucking pasture and let them have at it.

The only reason to keep them apart is if they were of opposite sex and would mate otherwise. Or perhaps if they fight too much.

But as I said. Goat cheese. Ok. Goat pie, not so much. So they both have to be females. And I am pretty sure females wouldn’t fight much.

So, no ropes, no chains, no fences, two goats and a fucking circular pasture.

And you wonder why people hate math?