### Microsoft's Puzzle: A Challenge

#### By dcb on Feb 19, 2005

If you enjoy solving puzzles and word problems you might enjoy reading the book called:

*How would you move Mount Fuji?*

This book contains a collection of various types of logic puzzles, design question, estimation challenges, and choice dilemmas that, according to the author, Microsoft (and others) use during interviews with new grads. The theory is that since these folks don't have a lot of industry experience or a proven track record of success, that creative thinking under pressure (a critical success factor) can be determined to some extent by observing a candidate's process of dealing with a challenging scenario to which they haven't previously been exposed.

To me, these kinds of problems provide for a fun distraction now and then.

I'm pretty good these these, but here's one that got me. Sometimes the apparently simple ones are the hardest because you can convince yourself of the one-true-answer and can't see beyond your solution. Give it a try!*How many distinct points are there on the surface of the Earth from which you can walk one mile due South, then one mile due East, and then one mile due North, and end up at the same exact spot from which you started?*

It isn't a trick question, per-se. Use basic assumptions, such as walking on the surface of (not thru) the Earth, that magnetic and true North are the same, that the Earth is a smooth perfectly spherical "globe", etc. Don't make it harder than it is. According to the book, you'd be disqualified from further consideration for a job at Microsoft if you came up with "zero" or "one" point.

In case you give up, here is the solution:

http://blogs.sun.com/roller/resources/dcb/SOLUTION_3_Legged_Trek.html

Posted by

Dave Brillharton February 19, 2005 at 09:01 AM EST #Posted by

Kevinon February 19, 2005 at 12:27 PM EST #I think the answer is the set of points comprising:

- the point of north pole

For reasons by described in comment by David

- The circle approximately coincident with the latitude of 89°57'46'' South.

By my rough calculations, the above latitude happens to lie 1 mile north of the southern latitude of the earth which has a circumference of 1 mile. Hence traveling east 1 mile on that latter latitude would bring you back to the same point. ;)

(Using the polar diameter of 12720km to roughly calculate circumference of earth and km/degree).

Does that solution seem correct? Any other solutions?

Posted by

Paul Jakmaon February 19, 2005 at 04:30 PM EST #Posted by

Dave Brillharton February 19, 2005 at 10:33 PM EST #Ah, of course, all the latitudes whose circumferences are 1/2n mile for n=0 to n=infinity would also have a corresponding latitude lying one mile north. The distance between each latitude tending towards 0 pretty quickly though ;).

Course :)

So, how exactly would you move mount Fuji then (according to MS at least). Depending on the exact criteria (particularly the definition of 'move') one answer could be "wait", for Fuji is always moving - as the earth does. ;)

Posted by

Paul Jakmaon February 20, 2005 at 11:29 AM EST #Posted by

gueston September 20, 2006 at 06:32 PM EDT #