Suppose that P(x) is a polynomial of degree 8 with real
coefficients, and
P(k) = 1/k for k = 1, 2, 3, 4, 5, 6, 7, 8, 9.

What is P(10)?
What is P(11)?

>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, March 4,
1999.
Submit solutions to Prof. Hanna at mathprob@nadn.navy.mil, or via
the
mailbox in Chauvenet 301.



------------------------
The only midshipman to get the correct answer to problem #88 was
4/c
Cipriano, who failed to offer an explanation.  Another week when I
can
keep my dollar.  Bob needs only two rounds to determine Alice's
ten
numbers.  If he knows all her numbers are less than 10^k, he can
use
10^9k, 10^8k, ..., 10^k, 1, and Alice's response will list her
numbers
from left to right.  If Bob's first set of numbers is 1, 1, ...,
1, he can
easily find a k so that all Alice's numbers are less than 10^k.