The integers from 1 to 8 are formed into four pairs at random. Each pair
determines an interval on the positive x-axis.  What is the probability
that among these four intervals there is one that meets all the others?

(For example, if the pairs are {1,3}, {2,8}, {4,7}, and {5,6}, then the
interval [2,8] meets each of the three intervals [1,3], [4,7], and [5,6].)


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

A solution is "correct" if it answers the question correctly and explains
the answer; a solution is "best" if it includes the clearest correct
explanation.  Solutions are due by noon on Thursday, April 22, 1999.
Submit solutions to Prof. Hanna at mathprob@nadn.navy.mil, or via the
mailbox in Chauvenet 301.



-----------------------------
Correct solutions came in for problem #93 (the hemispherical cake), came
from Midn 1/c Dequeljoe and Wood and from Midn 4/c Stepp (whose numbers
seem to be a little off).  Prize to Midn Dequeljoe, whose solution is
posted on the bulletin board in the Chauvenet lab-deck corridor.