# Where are you?

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You are standing on the surface of earth.

You walk one mile south, then you walk one mile west, then you walk one mile  north and you are back where you started.

Where are you?

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The true north pole?

This can't be the answer; it's too easy.

Des Moines?

--Brant

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5 minutes ago, Brant Gaede said:

The true north pole?

This can't be the answer; it's too easy.

Des Moines?

--Brant

You wouldn’t want to choose Des Moines, Iowa as that would have you end at a spot just under a mile west of your start point, instead of at your start point.

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The North Pole works.

Other places work, too.

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On the equator.

--Brant

any line of latitude that's walkable to and from?

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15 minutes ago, Brant Gaede said:

On the equator.

--Brant

any line of longitude or latitude that's walkable to and from?

If you start on the equator you will end at a point over a mile west of where you started, instead of where you started.

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Meant to just say latitude.

Therefore I suggest the magnetic North Pole.

--Brant

and the South?

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3 hours ago, Brant Gaede said:

Meant to just say latitude.

Therefore I suggest the magnetic North Pole.

--Brant

Yes, the North Pole works.

There are more places.

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3 hours ago, Brant Gaede said:

Meant to just say latitude.

Therefore I suggest the magnetic North Pole.

--Brant

and the South?

You cannot start from the South Pole because you couldn’t then satisfy the first walking instruction.

north pole

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19 minutes ago, BaalChatzaf said:

north pole

And there are more.

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39 minutes ago, Jon Letendre said:

And there are more.

There are an infinity of more. Sets of infinities, actually.

:-)

J

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13 hours ago, Jon Letendre said:

You cannot start from the South Pole because you couldn’t then satisfy the first walking instruction.

I was positing the magnetic pole.

--Brant

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3 hours ago, Jonathan said:

There are an infinity of more. Sets of infinities, actually.

🙂

J

Yes.

There are an infinite number of additional solution sets and each one gives a specific infinite set of points on earth from which to start.

Only a handful of the solution sets are walkable, given the size of a person, but mathematically there are an infinite number of solution sets and each one provides a specific infinite number of starting points that will work.

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14 minutes ago, Brant Gaede said:

I was positing the magnetic pole.

--Brant

Those wander. We can stick to geographic poles for purposes of this puzzle.

Earth wobbles and so even the geographic poles wander slightly, so let’s assume a geometrically ideal sphere with stable poles defined as single points.

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That's an old riddle, I remember seeing it around 1960. Probably even much older.

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Just now, Max said:

That's an old riddle, I remember seeing it around 1960. Probably even much older.

I stumbled upon it last night.

I didnt even realize there were more solutions beside North Pole until after starting the thread!

I haven’t checked any resources, but Jonathan seems to see the same additional solutions that I do.

Dont spoil it or hint too much!!

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2 minutes ago, Jon Letendre said:

I didnt even realize there were more solutions beside North Pole until after starting the thread!

I think the puzzle originally was supposed to have only 1 solution, until people discovered more solutions.

2 minutes ago, Jon Letendre said:

I haven’t checked any resources, but Jonathan seems to see the same additional solutions that I do.

Dont spoil it or hint too much!!

Mum's the word.

Well, one suggestion: make a few sketches, that may help.

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I think of deception and switched meanings of words when I hear “riddle.”

I want to clarify that there is no trick, no switching the meanings of words.

Rather, the additional solutions are straight-forward solutions whereby the walking instructions can be followed plainly, as stated, and you end on exactly the spot on earth where you started.

When you hear and grasp the additional solutions you will not say it was a trick, just that you hadn’t thought of the little twist.

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Imagine a circle surrounding the South Pole as its center and exactly a mile larger in radius than a concentric smaller circle with circumference of exactly a mile around the South Pole.

Then there are an infinite number of starting points which satisfy the conditions.

But it doesn't sound to me like that's what you and Jonathan are thinking of.

Ellen

ADDENDUM: See this post, next page.  I realized a bit later that there's an infinite number of circle sets.

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I tried to do this in the Bermuda triangle a few centuries ago and look where I ended up.

(Imagine a quip like that on a site themed on Rand...  )

Michael

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7 hours ago, Ellen Stuttle said:

Imagine a circle surrounding the South Pole as its center and exactly a mile larger in radius than a concentric smaller circle with circumference of exactly a mile around the South Pole.

Then there are an infinite number of starting points which satisfy the conditions.

But it doesn't sound to me like that's what you and Jonathan are thinking of.

Ellen

Yes, that is one of the solution sets, a circle of latitude located a little bit more than one mile, about 1.1592 miles, or one and 1 divided by 2pi miles, north of the South Pole. An infinite number of starting points are on that circle  of latitude.

There are an infinite many more solution sets each one providing a specific infinity of starting point choices. But only a handful of the solution sets, about 50 maximum, are walkable - because it becomes that our feet are too large for it to be done accurately.

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1 hour ago, Ellen Stuttle said:

Imagine a circle surrounding the South Pole as its center and exactly a mile larger in radius than a concentric smaller circle with circumference of exactly a mile around the South Pole.

Then there are an infinite number of starting points which satisfy the conditions.

But it doesn't sound to me like that's what you and Jonathan are thinking of.

Ellen

I'm a bit confused.  It seems to me that since the lengths are equal, the three points must describe an equilateral triangle, so 60 degrees per side.  If you walk south then turn west, isn't the angle of that turn 90 degrees?  You won't end up at the same starting point.  I can see how it works at the north pole, but since you're not actually touching the south pole, and if you were to touch the south pole there would be no way to travel west to satisfy step two (once there you can only go north)...am I missing something?

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6 hours ago, 9thdoctor said:

I'm a bit confused.  It seems to me that since the lengths are equal, the three points must describe an equilateral triangle, so 60 degrees per side.  If you walk south then turn west, isn't the angle of that turn 90 degrees?  You won't end up at the same starting point.  I can see how it works at the north pole, but since you're not actually touching the south pole, and if you were to touch the south pole there would be no way to travel west to satisfy step two (once there you can only go north)...am I missing something?

The walk in Ellen’s solution does not make a triangle, and neither does the walk that starts on the North Pole.

The latter walk makes a large pizza slice shape, almost one sixth of a pizza. None of the angles in the shape are 60 degrees. The point of the slice has an angle of about 57.296 degrees, or 180 divided by pi degrees.

Back to Ellen’s solution, south one mile then a 90 degree turn to the right, so you now face west, is correct. If you then follow the rest of the walking instructions you will end at the starting point. You will walk one mile west, then you will walk one mile north and you will be back to the point from which you started,

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And there are more! Many more.

Hint: if one is ordered to walk west, one doesn't run out of westwardness just because one has circled back to the point where one began walking west. If it takes two trips, or thirty two, around a circle to equal a mile, then that's what it takes.

J