Brain Teaser No 1

Posted by: Don Atkinson on 16 November 2001

THE EXPLORER

An explorer set off on a journey. He walked a mile south, a mile east and a mile north. At this point he was back at his start. Where on earth was his starting point? OK, other than the North Pole, which is pretty obvious, where else could he have started this journey?

Cheers

Don

Posted on: 16 November 2001 by Greg Beatty
...at a point above the south pole such that, after walking a mile south, the circumference of the earth is exactly one mile.

Do I get the prize?

- GregB

Insert Witty Signature Line Here

Posted on: 16 November 2001 by Craig B
Why, the Mana Forum of course!

Bah

Posted on: 16 November 2001 by Greg Beatty
...couldn't be the Mana forum. I'm still banned from there so can't walk a mile south, etc.

- Greg still-banned B

Insert Witty Signature Line Here

Posted on: 16 November 2001 by Craig B
One cannot walk in a southward direction when one is at the south pole, now can one? One can only travel in a northward direction, at least at the start of ones journey.

The answer is obviously the Mana Forum, despited the fact that you personally are no longer permitted to make the journey.

Respectively,

Craig
PS. I believe that you have just inserted your own witty signature line!

Posted on: 16 November 2001 by Greg Beatty
...of course, about it not mattering (is that a word?) if I can personally make the journey or not.

But if you re-read my answer, you will no doubt realize that my proposed starting point is above the south pole and not on it.

- GregB

Insert Witty Signature Line Here

Posted on: 16 November 2001 by Don Atkinson
Pretty cool response Greg, unless of course you've been there big grin

Craig, GregB says

my proposed starting point is above the south pole and not on it.

perhaps if he had said 'north of' (which is what i'm sure he meant?) instead of 'above' ?

Cheers

Don

Posted on: 16 November 2001 by Tim Oldridge
On a rather big (certainly wide) ship steaming due West at walking pace.

OR (similar logic):

One mile due North of one of those running machines you see at the gym (orientated East/West of course)

OR (similar logic)

Insert appropriate glacier into journey

Timo

[This message was edited by Tim Oldridge on FRIDAY 16 November 2001 at 21:49.]

Posted on: 16 November 2001 by Craig B
Greg,

Must I draw you a picture. Whether you were levitating a mile directly above the south pole or a hundred miles above it in outer space, you still cannot travel in a southward direction across the planets surface. You could merely travel vertically (further out into space, as in your case, or closer to the planets surface at the pole) or northward.

If you have any further geoscientific evidence to support your case, then please submit it now, otherwise, the only reasonable answer thus far is the Mana Forum.

Respectively (still),

Craig

Posted on: 16 November 2001 by Craig B
wispering... Not so loud, we have a live one here.

Craig
PS. on second thought make that two live ones big grin

Posted on: 16 November 2001 by Don Atkinson
Still whispering,

probably best to leave GregB in suspense above the South Pole roll eyes

Cheers

Don

Posted on: 16 November 2001 by Greg Beatty
Ah!!! My nothern hemisphere bias creeping in - 'above' to me meant north - no doubt I'm guilty as charged.

OK - here's one.

David Dever didn't turn up at the demo at the Manchester show...

- GregB

Insert Witty Signature Line Here

Posted on: 17 November 2001 by bam
Ok,
Here's another teaser for you to mull on.

A woman is sitting in a boat in a small reservoir. In the boat with her is a hemp sack containing the dead body of her audiophile husband. She had become frustrated with her obsessive partner mainly due to the proliferation of ugly black boxes and metalwork that had taken over her living room. Not to mention the brick dust and ill fitting carpets where he installed the make-shift mains spur; nor to mention the devastation of her beautiful flower beds where he had insisted on driving a dozen copper pipes into the ground. The final straw came when, at the recommendation of an old school friend in the business (a friend before she met HIM), Ideal Home dropped in to offer to do a feature. Shocked by the hifi carnage they declined to do the feature.

Anyhow, I digress. She has weighed the sack down with two 135s and the twisted remains of his Mana stands and sewn it tightly with NACA5 (ensuring correct direction in the weave) to ensure he will sink without trace. Whilst securing the parcel she glaces over to the reservoir wall and notices a water level marker. With a major struggle she manages to heave the sack of hubby and hifi over board. After a while she settles back in the dingy and smokes a well-earned cigarette. The reservoir wall catches her eye again; she notices the height of the water line has changed.

Has the water risen or fallen against its original level on the water level marker?

BAM
(Hint: the answer is not "the Mana forum")

Posted on: 17 November 2001 by Don Atkinson
Bam,

I guess the water level would rise.

Dead bodies normally float ie less dense than water. (I don't have a lot of experience at this, but thats why you weight them down with 135s etc)

Floating bodies displace their owm mass of water (Archemedies??)

Forcably drowned bodies displace their own volume of water.

Tell me i'm wrong, and induce that sinking feeling!!!

Cheers

Don

Posted on: 17 November 2001 by Martin Payne
The boat floats by displacing an amount of water weighing the same as that of the boat and contents.

When the body + weights is heaved overboard it sinks because it displaces less water than it's weight.

Less water is displaced, the water level goes down.

cheers, Martin

Posted on: 18 November 2001 by Don Atkinson
Bam,

Serious doubts about my first answer above.

Going for a bath. Will give it more thought! Might have to get dictionary to spell eureka properly !

Don't post your answer yet - please.

(of course Martin P is correct,providing the 'body' does sink and not just float beneath the surface, but I need to satisfy myself about the physics)

Cheers

Don

Posted on: 18 November 2001 by Don Atkinson
I enjoyed the bath, although Mrs D isn't too impressed with the indelible ink marks on the enamel. The girls are also really worried about me playing with toy boats, and tying lumps of lead solder with string round the necks of their Barbie dolls!!!!

Yep Bam, Martin P is right. The water level FALLS given your two conditions, that a) the body sinks and b) the water level changes. IF the weighted body just floated beneath the surface ie it had the same density as the water, the water level would not change, but that was not one of your conditions.

And of course if you only had a 250, instead of a pair of 135s, well, the body wouldn't sink at all, would it. In fact it would probably float with a good bit of the evidence clearly visible above the water level..... shows the true value of the deeper bass of 135s......and the water level in the reservoir would no doubt rise..........or would it? Me thinks that under these circumstances the water level wouldn't change.....??

Cheers

Don

Posted on: 18 November 2001 by Alex S.
also leaves you back where you started but more tired.

Alex

Posted on: 18 November 2001 by Martin Payne
quote:
and the water level in the reservoir would no doubt rise


Don,

the water level will never rise under any circumstances.

The initial conditions are that all items are in a boat.

Anything you throw overboard will either sink or float.

Anything that sinks is denser than water. Less water will be displaced. The water level goes down.

If something is lighter than the water, it will buoy up in the water until the same wieght of water is displaced as the weight of the object. It doesn't matter how much less dense it is than the water, it will float upwards until the same weight of water is displaced.

Given that all items start in a floating boat, the water level can only ever go down, and not up.

cheers, Martin

Posted on: 18 November 2001 by Don Atkinson
Martin P,

You say Given that all items start in a floating boat, the water level can only ever go down, and not up.

Yep, I agree, which is why I wrote, in a pathetic attempt to get others to think :-

Me thinks that under these circumstances the water level wouldn't change.....??

I think we're all agreed with you now, if the body is dense enough to sink, the water level falls (the more dense, the greater the fall). If the body has the same density as the water, or is less dense than the water, the water level remains constant. The water level never rises (as you say).

Can't even begin to wonder why I got it wrong to start with....but what a waste of a pair of 135s....can't say the same for the remains of the Mana.....

Cheers

Don

Posted on: 18 November 2001 by Craig B
The volumetric water displacement of a floating vessel is referred to as its draw. A vessels draw is a function of its weight and its buoyancy.

A submerged object, on the other hand, displaces only its volume, its weight has nothing to do with it.

Throwing perfectly good Naim amps and assorted bits overboard with the remains of ones uncooperative spouse attached will not cause the boat to rise by an equivalent volume of draw as that of the castoffs volume. The boat will only rise by the amount of its reduced weight to buoyancy ratio. If the boat were merely load reduced by the amount of the removed 'cargo' then the water level of the reservoir would indeed drop, however, the cargo enters the water and displaces its volume equivalent which is greater than the reduced mass effect upon the buoyant vessels draw.

The water level in the reservoir will indeed rise but only by the volumetric difference between that which has been cast overboard and that of the reduced draw of the boat. However, I doubt that the murderous wife would notice any appreciable difference on the marker.

Someone give Inspector Morse a ring. As a fellow Naimer he will no doubt be keen to get to the bottom of this.

Do I win a record?

[This message was edited by Craig Best on MONDAY 19 November 2001 at 13:00.]

Posted on: 19 November 2001 by bam
Craig, I made need Morse's help to fully understand your argument! However, if you are saying the water level might rise then I am sorry to say no record for you.

Martin had it right from the start. Don "Archimedes" Atkinson's bathroom antics, whilst moderately disturbing, got him there in the end. Well done. big grin

I hope this story serves to remind you of the importance of maintaining a happy hifi household.

Posted on: 19 November 2001 by Craig B
I'm relieved actually, as I had made the whole thing up and would have felt bad had I guessed right in the end.

Craig (with a clean conscience but still wondering where the explorer started exploring from)

Posted on: 19 November 2001 by Don Atkinson
Try starting approximately 1 and 1/6th of a mile north of the South Pole. (it really needs to be 1 and 1/(2pi) from the South Pole).

Does this help?

You could start a bit closer to the Pole, but you would then have to walk twice round the Pole to do the '1 mile east' bit!

Does this confuse ?

Cheers

Don

Posted on: 19 November 2001 by Don Atkinson
Bam, a nice little teaser.

Mrs D has threatened to try the experiment herself, if I don't return the bathroom to it's former glory!

Cheers

Don

Posted on: 19 November 2001 by Tim Oldridge
"Try starting approximately 1 and 1/6th of a mile north of the South Pole. (it really needs to be 1 and 1/(2pi) from the South Pole).
Does this help?

You could start a bit closer to the Pole, but you would then have to walk twice round the Pole to do the '1 mile east' bit!"

Don

I still prefer the glacier solution.

Timo