Call a set of positive integers "friendly" if, whenever it contains a
positive integer x, it also contains either x+1 or x-1 (or both.)
(So {1, 2, 108, 109} is friendly and {1, 2, 100, 109} is not.)

How many different five-element subsets of {1, 2, 3, . . ., 109} are
friendly?

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All midshipmen submitting correct solutions to problem #109 by noon on
Tuesday, February 15, 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 #108 (size of a ball touching three stacked
cannon balls) came from Midn 2/c Larson and 4/c Milev. Mr. Larson's
solution is posted on the bulletin board in the Chauvenet lab deck
corridor.