John Korb's recent request for help with the quadratic equation
reminded me of a problem that my math teacher set "...as a piece of
light summer recreation until we meet again in September." (The guy had
a sense of humor!). I've not been able to solve it in almost 30 years!
 
A perfect goat is tethered by a perfect rope at the edge of a perfectly
circular field. The field is enclosed by a (perfect) fence such that
the goat can not stray outside the confines of the field. How long must
the rope be in order that the goat can eat exactly half the surface
area of the field?
 
This will be a band-width waster for those who choose to try it, both
in terms of 3000-L, and also mental bandwidth. However - I'd be
fascinated to see if there are any solutions out there.  FWIW the only
person who solved the problem over the summer went on to become a
Turing Fellow, and wrote a major book about Alan Turing.
 
Good luck - gentle-persons, start your minds!
Tony