Well, I just got back from interviews at Microsoft. They went great, and I had lots of fun. Here's one of the questions that one of the interviewers asked. I managed to work it out:

"Mathematically describe all points on the globe where you can go one mile south, one mile west, then one mile north and end up where you started."

Terry

the north pole is one point and this is the non-mathematical answer

the other points are just north of the south pole, being one mile north of every point on a meridian (and in between meridians) where the circumference of each latitude is one mile, whihc would allow you to wlak for a mile and return to the point where you started, and if I can remember formulae from 30 yrs ago .. it would be every point one mile and 840 ft 4 in north of the south pole

circumference = 2 x pi x r
circumference = 1
r = 1 / 2 x pi
r = 0.159 miles where pi=3.1415926535
0.159 miles = 840 ft 4 in where mile = 5280 ft
the points = 1 mile plus 840 ft 4 in north of the south pole

if I've remembered the formula wrong or the a mile is not 5280 ft, then the answer will be a little different

.. and my typing is awful

whihc = which
wlak = walk
or the a mile = or a mile

DARN, gtho4 just beat me to it. That's exactly what I was going to say

golddragon,
the measurements used might be a bit wrong, as the earth is curved, not flat!

Yep, that's the idea! You missed some points though.

hint: What happens if you head west and pass your starting point 10 times and end up where you started? 20? 50?

[This message has been edited by Terry (edited 04-30-2000).]

never thought of that! presumed that one circumference of the globe = a latitude with a distance of one mile, would be the limit .. unsafe to presume

which means that depending upon the definition of "a point" on the surface of the earth you would end up with innumerable answers to the question (I think) .. and depending upon the width of your shoes, so that each answer (or each point) does not involve going over trodden ground (sic!), that's my initial reaction, will think about it

golddragon, your turn mate

.. thought a formula in the shower this morning!

p = the point we require
q = the point one mile south of p
r = distance from q to s
s = the south pole
c = circumference of a latitude at q

as r = c / ( 2 x pi) then, since p = 1 + r, the mathematical description is:

p = 1 + c / ( 2 x pi)
where the reciprocal* of c is an integer from 1 upwards

* in addition to the p calculated where c=1, the other answers for p will vary with each other value of c between 1 and zero (excluding zero and 1), being those values for which the reciprocal of c is an integer e.g.
if c = 1/3rd of a mile, then you walk along that latitude three times
if c = half a mile, you walk "around" twice
if c = 1/70th of a mile, you walk around 70 times
etc etc ad infinitum .. I think

Terry, what answer did you give them .. did you get on the short list .. are you at liberty to tell us?