Six friends have just experienced a small disaster while exploring a cave.
They now have to traverse a particularly difficult passage with only one
light.

At most two people can make the trip at once. (There's a narrow ledge.)
They must take the light with them and they must travel at the speed of
the slower person. Then someone must return with the light so that two
more people can cross.

It takes Alice 3 minutes to make the trip (in either direction; 6 minutes
round trip). Bob needs 4 minutes, Charley 5, Danielle 6, Elizabeth 7, and
Frank 8 minutes. What is the shortest time needed for all six people to
get across?

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All midshipmen submitting correct solutions to problem #107 by noon on
Tuesday, January 25, win a cookie. The best solution will be posted on the
problem bulletin board.
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A solution is "correct" if it has the lowest time submitted and explains
how that time is possible. 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 solutions to problem #106 came from Midn 3/c Heineike and 4/c
Milev and several math profs. 2/c Rivera, 2/c Larson, and 4/c Jaskowiak
found all the positive solutions. The easiest trick is to note that if
xy=x+y+2000, then (x-1)(y-1)=2001. There are 8 different positive integer
divisors of 2001.