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        riddles >> medium >> Globe Traversal Solution
        
(Message started by: Otto on Jul 23^rd, 2002, 9:13pm)

Title: Globe Traversal Solution
Post by Otto on Jul 23^rd, 2002, 9:13pm

[This is "cheating" in some sense.]

You can start from any point on the globe and travel any direction
initially. Since all the points on the globe are the same, either no
point or every point satisfies this riddle. Since the "hint" asserts
that more than two points satisfy it, all points do.

Title: Re: Globe Traversal Solution
Post by QM on Jul 23^rd, 2002, 9:50pm

Actually, I think that this is a sphere with poles, not all points are equal. In particluar, the north and south poles are distinct. It might be that the answer could be all the points on the equator, but no others. (That's not the answer, though.)

Title: Re: Globe Traversal Solution
Post by Ivo on Jul 23^rd, 2002, 10:00pm

There's a circle of points very close to the south pole that also work....

Title: Re: Globe Traversal Solution
Post by Ctrl-D on Jul 23^rd, 2002, 10:19pm

I'd say that the north pole works, as well as a ring of continuous points 1 mile north of the point in the southern hemisphere where the circumference of a cross section is 1 mile as well.

^D

Title: Re: Globe Traversal Solution
Post by xixi on Jul 23^rd, 2002, 11:21pm

Ctrl-D is right. However, there are actually more points. Not only can one start at any point one mile north of where, in the southern hemisphere, the circumference of the cross section of the globe is one mile, one can start one mile north of where the circumference is half a mile or a third of a mile or (1/n) miles, where n is a positive integer. This is because walking east one mile along any of these paths will result in the circumnavigation of the globe n times, leaving the traveller one mile south of his original starting point.

~xixi

Title: Re: Globe Traversal Solution
Post by Franklinstein on Jul 28^th, 2002, 11:10am

excellent answers. I am curious about the second hint, though: Christopher Columbus. Perhaps there is a trick here involving the magnetic equator. Which way does a compass point when it is between the magnetic poles?

Title: Re: Globe Traversal Solution
Post by BigBadBert on Jul 29^th, 2002, 12:42pm

Answer 1=
The North Pole-
Go south for one mile, walk clockwise (if looking at the earth from the top) in a circle, (maintaining a distance of one mile from the pole) for one mile, turn toward the pole and walk toward it (north) for one mile.

Answer 2=
Any point that is 1.16 (approximately) miles away from the South Pole-
The circumfrence of a circle is pi times the diameter we need a circle with a circumfrence of 1 mile. So 1 divided by pi (3.14 because I want to keep the numbers small) equals .32 (rounded). So we cut that in half to get the raduis which would be .16 . So from 1.16 miles away from the South Pole, we go south for one mile, walk west around our 1 mile circle, then walk north 1 mile to or original location.

Title: Re: Globe Traversal Solution
Post by BigBadBert on Jul 30^th, 2002, 5:53am

Actually, just thought of another set of solutions based on my second answer. walk a mile south toward the South Pole, walk west around a circle of 1/2 mile diameter, then walk north 1 mile. Will work for any circle of 1/n length where n=a positive whole number.

Title: Re: Globe Traversal Solution
Post by nlgordaz on May 13^th, 2009, 8:54pm

How is it "cheating?"

Title: Re: Globe Traversal Solution
Post by towr on May 13^th, 2009, 10:43pm

on 05/13/09 at 20:54:34, nlgordaz wrote:

How is it "cheating?"

It's not, Otto was just plain wrong. But xixi had the right answer.

Rather old topic to resurrect..