[last problem this semester]

The owner of a square plot of land 100 meters on a side knows that a
telephone wire is buried 30cm deep along some straight line that crosses
at his land.  He could locate the wire by digging a ditch along the sides
of his property, which requires 400m of ditch.  But digging along just
three sides of the property is also guaranteed to find the wire, and that
takes just 300m of ditch.  What is the shortest total length of ditch he
needs to dig to guarantee that he will find the wire?  (If you prefer to
imagine finding the wire electronically, what is the shortest total path
length over which he needs to move his detector to guarantee that the wire
is directly underneath the detector at some time?)

is directly underneath the detector at some time?)

(This is Macalester College Problem of the Week #865.)

There will be a $1 prize for the midshipman who draws or describes the
shortest ditch which is guaranteed to work.

Solutions are due by noon on Friday, December 4, 1998.  Your solution
should include the length of your proposed ditch.  Submit solutions by
e-mail to mathprob@nadn.navy.mil or on paper to Prof. Hanna's mailbox in
Chauvenet 301.

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No midshipman submitted a correct solution to problem #81.
Since there are 252 different 5-language subsets of a set of 10 languages,
it's possible for 250 people to speak only 10 different languages among
them and still have, for every pair of people, at least one language that
one speaks and the other doesn't. It's not particularly easy to see that
10 is the smallest number that works.