## October 15, 2008

### Microsoft's Puzzles

How many points are there on the globe
where, by walking one mile south, one
mile east, and one mile north,you reach
the place where you started?

Anonymous said...

There are an infinite number of points on a the globe for which this true. The North Pole is one point, but there are many points that are exactly (1 + 1/2pi) miles away from the South pole. If you walk 1 mile south, you will be 1/2pi miles away from the south pole. A one mile walk east will bring you in a full circle around the South Pole. Then when you walk one mile north, you will be in the same place that you started.

James Brooks
jdbrooks3@yahoo.com

Secret Squirrel said...

James, you're almost there! You could also be (1 + 1/4pi) miles N of the S pole. You could then walk 1 mile S, 1 mile E (circling the S pole twice), and 1 mile N back to where you started.

It follows that there are an infinite number of distances (latitudes) from the S pole from which you can start - (1 + 1/2pi), (1 + 1/4pi), (1 + 1/6pi), etc, with the number of required "laps" of the pole being 1, 2, 3, etc.

Arvind said...

I guess the 3 points are: North Pole, South Pole and Equator.

Arvind said...

Correction. There's only one point and that's called the Equator!!

Anonymous said...

but aren't there a ton of places on the equator? i mean, it goes all around the world!

Evan said...

Nice job correcting yourself; you cannot walk south away from the south pole. But you're still wrong. The first two answers were correct.

Kiklibio said...

ow :( didnt come up with the answer. better luck with the next one :D

btw just out of curiosity... how do you come up with the 1/2pi? Do you look up what distance from the S pole equals 1 mile? or is there somesort of mathimatical way to find it?

kind regards

Beca said...

Microsoft sucks but arvid is correct.