We have ten beads numbered 1, 2, . . ., 10. We select them in random order
and put them on a string to make a bracelet.

* Is it always possible to find three beads in a row whose numbers
add up to at least 17?

* Is it always possible to find three beads in a row whose numbers
add up to at least 18?

* Is it always possible to find three beads in a row whose numbers
add up to at least 19?

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All midshipmen submitting correct solutions to problem #103 by 3:30 pm on
Tuesday, November 14, 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 a correct answer to at least one of
the questions and explains why it is correct; a solution is "best" if it
includes the clearest correct explanation.  Submit solutions to Prof.
Hanna at mathprob@usna.edu, or via the mailbox in Chauvenet 301.

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Problem #102 (cutting the square into two rectangles) produced only one
(complicated) solution. The shortest side of the smallest rectangle has
length 2 - sqrt(3). Mdn. 4/c Milev earns another cookie.