Find the maximum possible value of the product 

        (1-x)(1-y)(1-z)

for positive numbers x, y, and z such that x^2 + y^2 + z^2 = 1.

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All midshipmen submitting correct solutions to problem #111 by noon on
Tuesday, March 28, win a cookie. The best solution will be posted on the
problem bulletin board.
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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.




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Correct answers to problem #110 (random pieces on a chessboard) came from
Midn. 4/c Jaskowiak, Milev, and Scheid-Young; only Midn. Scheid-Young
included an explanation, which is posted on the bulletin board in the
Chauvenet lab deck corridor.