Riddle

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Posted: Sat Jul 21, 2007 7:02 pm

Peanut:

Thanks for disproving math. I hate math.

As for the extra dollar, there was a probably a lawyer involved Very Happy

Posted: Sat Jul 21, 2007 8:17 pm

Quote:

I will of course eat humble pie if you can find a scenario my method gets wrong.

Now why would I want to do that, you used your brain, that's all puzzles are for Laughing

About yours, that's an endless equation in R1 and R2, but solvable, maybe a rainy day, it's now close to 100 degrees and my attention span gets a bit shorter then Laughing

Master Baiter Joined: 04 May 2007 Posts: 139

Quote:

You have a circular lawn. You wish to tether the goat to one edge of the lawn so that he can eat exactly half of the grass. How long should the chain be in terms of the radius of the lawn? You can make the standard assumptions, such as that the goat is infinitely small and so forth.

In this puzzle, we have two circles that overlap (the lawn and the goat's tether). This overlap must be exactly half of the lawn circle.

The simple answer (and depending on how you look at it, a cheat) is to attach the goat's chain to a post at the edge, then run it through a ring in a stake somewhere in the lawn such that the excess chain forms a circle completely bounded by the lawn and is 70.7% of the radius of the lawn. In this case the chain can be anywhere from twice that (1.4x the lawn's radius) to the diameter of the lawn.

Posted: Mon Jul 23, 2007 5:43 pm

LOL I'm doing difficult Laughing

I give up

Posted: Mon Jul 23, 2007 7:50 pm

thud419 wrote:

... You have a circular lawn. You wish to tether the goat to one edge of the lawn so that he can eat exactly half of the grass. How long should the chain be in terms of the radius of the lawn? ...

Working on the assumption that this involves Pi, that chain will be impossible to make. Why? The length of a chain in finite. It is measurable. It has an end (two in fact) and an exact length. The exactness of Pi on the other hand is (most probably) infinite. Even with a Cray supercomputer, you would spend the rest of your life trying to find the right spot to cut the chain and fail. Nobody will ever get it right.

One can probably *express* how long it should be, using π, but the chain will never be manufactured, at least not correctly.

Baiting Guru Joined: 04 Jan 2006 Posts: 3193

Apart from the fact that all things, even pi, can be stated to three significant figures...

Chains are already made in terms of pi. Each link is made from a pieces of steel rod of a certain length, which is then bent into a circle. The length of the steel rod becomes the circumference of the circle, and the diameter of the circle determines the length of the link. So the length of the chain of n links is

length = n * rod-length / pi

(Neglecting the diameter of the rods)

Posted: Tue Jul 24, 2007 11:15 am

thud419 wrote:

I realised my mistake after I'd gone to bed. You can remove three bags before the second weighing.

Weigh 1 2 3 4 vs 5 6 7 8
If unequal, label all bags on the light side L, and on the heavy side H
--8<------
really really complicated explanation - may work but I didn't read it ;
-->8------
that is the faulty bag.

Thud, you're overcomplicating things here.

1) weigh 6 against 6 bags. The side going up has the faulty bag.
2) From those 6, weigh 3 against 3. The side going up has the faulty bag.
3) From those 3, put one bag on each side of balance. If one side goes up, that's the faulty bag. If it stays in balance, the 3rd bag is the faulty one.

Baiting Guru Joined: 04 Jan 2006 Posts: 3193

^^^ But you don't know if the faulty bag is light or heavy. So on each weighing you don't know if the light side or the heavy side has the faulty bag.

Edit: VVV Laughing

Posted: Tue Jul 24, 2007 12:58 pm

Let me get this straight.. you put the goat on one side, three bags of gold on the other.. stick the potato up your arse and pick up the coins.. no wait, I've missed something

Posted: Tue Jul 24, 2007 1:02 pm

Order a Pizza first Laughing

Posted: Tue Jul 24, 2007 1:27 pm

thud419 wrote:

^^^ But you don't know if the faulty bag is light or heavy. So on each weighing you don't know if the light side or the heavy side has the faulty bag.

whoopsy! I thought I read the faulty bag is lighter. My mistake.

Posted: Tue Jul 24, 2007 8:20 pm

thud419 wrote:

Apart from the fact that all things, even pi, can be stated to three significant figures ...

Let's tell the people at Cray that. Man, they've been wasting *tons* of CPU calculating pi past 3.14. Laughing

Posted: Tue Jul 24, 2007 9:24 pm

It's not so difficult, forget Pi or � and write 22/7 and you're very close with your calculations.

Posted: Wed Jul 25, 2007 3:33 am

Okay KD, I'm a civil engineer. From time to time I calculate the amount of stormwater that can run through a circular pipe. But in order to do this I must know the cross-sectional area of the pipe. The formula for the area of a circle as I'm sure we all know involves pi, which cannot be computed exactly because it never repeats itself out to an infinite number of decimal places (so the mathematicians tell us). Yet, the pipe surely has a finite area. So how do I calculate a finite area using a formula with a indeterminate variable? This is the point where I usually hyperventilate, but in the engineering world, the answer is, I get it close enough to serve practical purposes.

Baiting Guru Joined: 04 Jan 2006 Posts: 3193

Pi is neither infinite nor indeterminate. It is merely irrational. As is all this head-scratching.

The fact that you don't know it's exact value is no problem, because you know it's value to any accuracy you could possibly want.

diameter of pipe: 3m (around 10 feet)
pi = 3.14159
area = pi.d = 9.42477 m2

This is almost certainly close enough for any reasonable use. To find out how accurate we can use a more accurate value of pi and compare the two answers:

diameter of pipe: 3m
pi = 3.14159265359
area = pi.d = 9.42477796077 m2

The difference between the two is the error we would get using the first value of pi. It amounts to 0.00000796077 m2, which is 7.9 mm2, or an error of less than one part in a million.

In KD's terms Wink

it's one character of 7 point text on a circular page ten feet across, or one character of 0.7 point on a circular page 1 foot across. Which is probably comparable to the size of a normal 10 or 12 point full-stop (ie period) on a page of A4/letter.

If that is not good enough, then we can use the second value of pi, accurate to 12 figures. To find out how accurate that is we use a more accurate value of pi:

diameter of pipe: 3m
pi = 3.1415926535897932384626433832795
area = pi.d = 9.4247779607693797153879301498385 m2

The difference between the last two is 0.6 micrometers2

Posted: Wed Jul 25, 2007 9:39 am

Another Riddle: (very silly answer)

If you were locked in a concrete room, with no windows and no doors, and all you had inside the room was a table and a mirror, how would you get out?

Our camp leader person thing told us this and when she told us the answer we all Rolling Eyes

No googling!

another pretty easy one..

If you have it, you want to share it. If you share it, you don't have it. What is it?

Baiting Guru Joined: 04 Jan 2006 Posts: 3193

I don't need no mirror, just give me a table.

Posted: Wed Jul 25, 2007 11:30 am

thud419 wrote:

(..)
diameter of pipe: 3m (around 10 feet)
pi = 3.14159
area = pi.d = 9.42477 m2

(..)

Tssk Tssk. circumference = pi * d .

Area = pi * d^2 / 4 = 7.0686 m2

@Reaper: 1) climb out over the wall ? (If the room has no doors or windows, you must have gotten into it somehow I guess)
2) I know what it is but I can't tell you.

Baiting Guru Joined: 04 Jan 2006 Posts: 3193

The accuracy will be the same though, since pi is not squared.

Posted: Wed Jul 25, 2007 8:09 pm

I was actually only being jokingly speculative about the chain never being the right length. According to thud419 the goat is, after all, infinitely small, so why not get the chain to follow suit ... Wink

thud419 wrote:

... it's one character of 7 point text on a circular page ten feet across ...

Hmmm, capital W or small i?

(And don't bullshit with fixed-width characters Laughing

)

[edit:] Pi R Squared? No, pie Are Round. Brownies are square. (sorry, couldn't resist.)

Posted: Wed Jul 25, 2007 9:21 pm

@ reaper
Rub your hands together until they're sore. Saw the table in two. Two halves make a whole. Climb through the hole.
What the hell is the mirror for? And how did they lock him in if there's no doors? Aaaaah - gotcha!

Posted: Wed Jul 25, 2007 9:36 pm

thud419 wrote:

because you know it's value to any accuracy you could possibly want.

That was my point exactly.

Posted: Thu Jul 26, 2007 12:16 am

@ Reaper. I assume the answer was that you couldn't have got in to the room? Although that's not necessarily true if the concrete was set around you. Then I don't know how you'd get out.

Baiting Guru Joined: 04 Jan 2006 Posts: 3193

@Gorden, I'd love to know what the mirror is for too.

Since it's a concrete wall, I'd rub my hand there instead, it's quicker and you only need one saw.

Once you're outside, shout yourself hoarse, and then ride off on the horse. That way they can't catch you.

Posted: Thu Jul 26, 2007 6:46 pm

any chance of getting this thread past a 100 posts? it'd be a first for me...
Pretty please? Smile