A large number of points are scattered in a plane. No two pairs of points
are the same distance apart. If you draw line segments connecting each
point to its nearest neighbor, what is the maximum number of line segments
any one point might lie on?

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All midshipmen submitting correct solutions to problem #112 by noon on
Wednesday, April 12, 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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No one submitted a correct answer to problem #111 (maximizing
(1-x)(1-y)(1-z) for (x,y,z) positive and on the unit sphere). The problem
turned out to be much more difficult than I thought. The maximum occurs at
x = y = 1/sqrt(2), z = 0, which doesn't actually meet the requirement that
x, y, and z be positive.