Friday problem...

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You start off at a point on the earth's surface.

You walk one mile south, then one mile east, then one mile north. You end up back where you started.

How many points on the earth's surface satisfy the above criteria?

 

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Everywhere in Holland.

FACT.

 

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Both wrong.

 

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Edited to remove stupidity. It is impossible to walk south from the south pole, or north from the north pole.

Ok. Substitute 'Travel by any means necessary' for walk.....

Are we talking about a place called 'One Mile South'?

Nope - there are no hidden meanings/clever wordplay in the question.

 

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Answering, "The Equator" is true if you were to say that you end up on the equator again, though actually you would be on the ewuator, you would still be 1 mile west of your origonal location.

Well its not true then, is it, since you're not back where you started....

There are two correct answers. One is the Notrh Pole. "North and South" are not "up and down," it is moving toward the respective pole. Therefor, traveling one mile south of the North Pole, traveling any distance west or east, then one mile north, would put you back at the North Pole.

Nope.

The other, less common answer, is that there are an infinite number of places on the Earth, where you would end up at the starting location if you were to travel one mile south, west, then north. And that is anywhere 1.159 miles north of the South Pole. You would travel south for one mile, putting you at .159 miles north of the South Pole. Then traveling one mile west would cause you to make a complete circle around the South Pole, ending where the westward mile started. Then travel one mile north and that would put you back at your original starting point.

Give this man a banana.

 

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Plagiarism is bad, ok?

Shocking.

 

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WTF? So if you are 1 mile south of the north pole and you walk straight, will you go on forever on the same path?

Well, in theory, yes. If you travel directly away from the south pole (any distance), make a 90 degree turn (left or right, doesnt matter), and start walking then you'll keep retracing the same steps for ever.

Sounds weird, but not if you imagine walking far enough that you end up on the equator - then turn 90 degrees and you just keep travelling round the world in perpetuity. (Geographic difficulties notwithstanding...)

 

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Maybe I'm being dumb (probably) but how does this one not work and the second one does its based on the same principle is it not?

Aero

Your case is indeed true, but the question was 'How many points', not 'Can you name one'

 

[Visage]

Cheers thats what I was after (I was being dumb = not surprised) I got caught up in the wording, So the answer is infinite?

Aero

Yup. Ive always assumed that it was one as well - the north pole, as you stated, but a colleague pointed out the other cases to me this morning...

 

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there are infinitely many points that you can do this from.

Thanks.

 

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Wouldn't it be finite, not infinite? Eventually you'd do the same one again.

Nope. There are an infinite number of points on the earths surface that are (1 + 1/(2n*pi)) miles from the north pole. Each value of n gives you a line of latitude, on which there are an infinite number of points.

 

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Having trouble with that, as there isn't an infinite number of points on the earth.

OK....lets turn that on its head.

If there are a finite number of points on the earth then:

a) How many are there?
b) What exists between these finite points?

 

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Talking in terms of the problem in the OP, for me each point would be around a size 10 shoe in size, making it around 12". By my calculations meaning a maximum of 5280 points on a circular mile around the north pole. There would be nothing between these points, as I'd be taking fairy steps

Dammit. You got me.

 

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The answer to the first riddle is an infinitie number of points.

The rationale being that if your starting point is 'anywhere on the earth's surface' and in following the directions still remain on the earth's surface then you are still meet the criteria of being anywhere on the earth's surface and so in effect are at the same place where you started i.e. the earth's surface.

Is this right?

Right answer, wrong reason, because the first line of the riddle stated 'a point on the earths surface', not 'any point on the earths surface'

 

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Technically would you not still be at 'a point on the earths surface'? Not the same point, but you would still be able to describe it as a point on the earths surface

I guess so. I think such an argument would be excluded when I said that the answer didnt involve any wordplay...

 

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There's an infinite number of points on just a one metre ruler.

Start counting with the two end points, then you've got the point at the 50cm mark half way between them, then the point at the 25cm mark half way between the 50cm and 0cm points, then the point at 12.5cm half way between 25 and 0, 6.25 half way between 12.5 and 0.

And you can keep finding points half way between your old points for ever (though they'll be at the 0.001mm and smaller value marks). So there must be a more than finite number of points as if you had say, 10000 points, you could find a new point halfway between any two adjacent points. Thus the number cannot be finite.

And obviously, there's a whole lot of one metre rulers on a one mile long line around the pole

You're assuming that space is infinitely divisible, which isnt in any way certain....

 

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I think it comes down to continuous vs discrete measurements.

Take a ruler and start at one end, now move halfway towards the other end. From this point now move half way towards the end of ruler from the new point.... If you repeat this you will never reach the end of the ruler no matter how many movements you make. You could therefore argue that there are an infinite number of points on the ruler.

its like saying that (1/2) + (1/4) + (1/8) + (1/16) + (1/32) + (1/64) + (1/128).......... etc = 1 at infinity.

In practice the number of points on a ruler is determined by the precision to which you can accurately measure the position on ruler. e.g. if you can measure to the nearest 1mm on a 30cm ruler there would effectively be 301 points on the ruler, if you could measure to the nearest 0.1mm there would be 3001. If you can meaure to a infinite precision there would be an infinite number of points (I think!)

The problem is when you try and translate a mathematical result (that there are an infinite number of points) into a physical reality - you may well find (and the jury is still out on this), that there is indeed a descreet structure to spacetime (on the Planck scale), so that there really are a finite number of points.

 

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i would assume that a point takes up space

This is where your reasoning fails. A point, by definition, takes up zero space.

 

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If you're only going to quantifiable space, rather than stuff made up by mathematicians to make their lives easier, then between points there is space. It is the space at atomic level between nucleus and electron

Which is certaibly quantifiable - how else would scientists be able to predict electron orbital radii?

 

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Well, eerm...good.