A right circular cone has a base of radius 1 centimeter and height 3
centimeters.  A cube is inscribed in the cone so that one face of the cube
is contained in the base of the cone.  How long is one side of the cube?

(From the 59th annual William Lowell Putnam Mathematical Competition,
December 5, 1998.)


There will be a $1 prize for the best correct solution submitted by a
midshipman.

A solution is "correct" if it answers the question correctly and explains
the answer; a solution is "best" if it includes the clearest correct
explanation.  Solutions are due by noon on Wednesday, January 20, 1999.
Submit solutions to Prof. Hanna at mathprob@nadn.navy.mil, or via the
mailbox in Chauvenet 301.


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The best solution to problem #82, finding the wire by digging a ditch, was
a joint solution by Midn. 4/c Elko, McKenzie, and Nollette.  Their
solution is posted on the bulletin board in the Chauvenet lab-deck
corridor.