There are 250 delegates to an international conference.  For every pair of
delegates, each speaks at least one language that the other does not.  In
all, the delegates speak N different languages.  What is the smallest
possible value for N which makes this possible?

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

A solution is "correct" if it gives the correct answer and explains why
that answer is correct.  It is "best" if it includes the clearest
explanation.  Solutions are due by noon on Thursday, November 19, 1998.
Submit solutions to Prof. Hanna via e-mail to mathprob@nadn.navy.mil or
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I have several unclaimed $1 prizes waiting in C317.