Alice and Bob work for the Acme Widget Company, and each participates in
one of the company's stock purchase plans.  Over a period of n months,
Alice invests a fixed number of dollars each month toward the purchase of
shares of Acme stock, while Bob purchases a fixed number of shares of Acme
stock each month.  Since the price of the stock fluctuates over time, Bob
may invest a different number of dollars each month, and Alice may
purchase a different number of shares each month, and may sometimes
purchase fractional shares.  There are no brokerage or other fees.

Who has the smaller average cost per share, Alice or Bob?

(From Konhauser, Velleman, and Wagon, Which Way Did the Bicycle Go?)

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 Thursday, October 15, 1998.
Submit solutions to Prof. Hanna at mathprob@nadn.navy.mil, or via the
mailbox in Chauvenet 301.

Midshipmen submitting correct solutions to two consecutive problems will
also win a text from the New Mathematical Library donated by Prof.
Novo-Gradac.

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Midn. 2/c Kistinger's winning solution to problem #75, the 13 triangles,
is posted on the bulletin board in the Chauvenet lab-deck corridor.  Each
of the triangles is a right triangle with legs having lengths in the ratio
2:3.