Microsoft's Puzzle: A Challenge

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

Comments:

Hint... If you're like me you quickly zeroed in on the North Pole. But, this is just one of many distinct points on the surface of the Earth in which this three-legged trek will succeed in returning to the point of origin. How many other points are there, and where?

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

Any point one mile north of the south pole also works since walking "east" at the south pole means spinning around. So there is a whole ring of points one mile north of the south pole where you can walk south to the pole, spin for a mile, and then walk back north to where you started (if you're not too dizzy from all that spinning).

Posted by Kevin on 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 Jakma on February 19, 2005 at 04:30 PM EST #

WARNING: ANSWER Good job Kevin (very close) and Paul (found a couple of the solutions, but not all)!! Starting at a point on the surface of the Earth 1 mile from the South Pole is not a legitimate answer. Because once you arrive at the South Pole, you can not proceed to "walk" eastwardly. Any forward motion whatsoever is, by definition, northward. And I just can't accept stationary spinning as a form of walking. However, that is very close to the answer, both in concept and in location. Had Kevin backed up an infinitesimal distance north, he would have found one "ring" that consists of an infinite set of solution points. For then he would have ended his southern directed 1 mile trek just north of the South Pole, and then he could have walked east. He would have completed a LOT of tiny circles around the South Pole, and if he worked it right, would have completed the 1 mile eastward trek exactly where he started that leg of the journey. And then he could follow his path in the snow (north this time) back to the exact starting point. There are an infinite number of points on that ring. Assume the number of tiny circles he made near the South Pole was "n" (where "n" approaches infinity as you get closer to the pole). Okay, now form another ring slightly further north of the previous ring. Just the right distance so, when you complete your southern trek, you are at the right distance from the pole to complete exactly "n-1" circles. Keep forming add'l circles until you get to Paul's ring in which "n = 1". As you can see, there are actually "I\^2+1" points that work, where I = infinity. The "+1" brings in the one point in the Northern hemisphere that also works, which is, of course, the North Pole (pick either true or magnetic north).

Posted by Dave Brillhart on 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 Jakma on February 20, 2005 at 11:29 AM EST #

very simmple

Posted by guest on September 20, 2006 at 06:32 PM EDT #

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