Part a)
There is a long path in a hilly area that winds around and finally end
back where it started - i.e. it is a long loop.  If you walk around
the loop clockwise, you immediately encounter a steep hill.  Climbing
the steep hill is about one quarter the distance of the entire walk. 
The remainder of the walk (in the clockwise direction) is a gradual
downslope until you reach the point where you started out.  Now, if
you walk counter-clockwise around the same path, does it take more,
less or the same amount of energy as it does to walk around the path
clockwise?

Part b)
Does a human being burn more caleries by walking in either direction?

Part c)
Several hours later, does the amount of caleries burned as a result of
the exercise differ if you walked in one direction or the other?  If
so, which direction causes the evenual burn of more caleries?

Hi jimvet-ga,

  Here are my comments to your rather interesting question:

-The immediate calorie burn in both directions should be
the same, since it involves rather same amount of energy.
-But I feel that traveling counter clockwise will help boost
the residual metabolic rate more than traveling clockwise, which in turn
will help burn more calories after the walk is over. This assumes
that no warmup is performed before the walk was started.  This
is similar to burning more calories, when you start with a warmup
and after some time start vigorous exercise.  You will not burn
more calories if you did it the other way. Again the duration of
the different parts of exercise plays an important role in the correctness
of this statement.
-Apart from the above, climbing a hill immediately, will tend
to put more strain on the muscles, which would create more pain
than a gradual slope followed by a steep hill.

Regards
ldavinci-ga