Four spherical cannon balls, each one foot in diameter, are stacked so
that each is touching the other three. There's room for a smaller sphere
(maybe the size of a baseball?) in the middle of the stack. How big is the
largest solid sphere that can be placed so that it's tangent to each of
the four larger spheres?


All midshipmen submitting correct solutions to problem #108 by noon on
Tuesday, February 8, win a cookie. The best solution will be posted on the
problem bulletin board.

A solution is "correct" if it gives the correct answer and explains why
that answer is correct. A solution is "best" if it includes the clearest
correct explanation. Submit solutions to Prof. Hanna at mathprob@usna.edu
(please no attachments!) or via the mailbox in Chauvenet 301.


                                
The best solutions to problem #107 (escaping the cave) came from Midn 1/c
Armstrong (cookie in C317), 4/c Jaskowiak, and 4/c Miller. A scheme
requiring 40 minutes is posted on the bulletin board in the Chauvenet lab
deck corridor.