> >> >Guidi Chan wrote:
> >> > > A fair die is rolled 2 times. X1 and X2 is the # of
> >> > > points showing on 1st and 2nd rolls.
> >> > > U = X1 + X2; V = X1 - X2.
> >> > > Show that U and V are NOT independent.
This question for some reason puts me in mind of a telephone call that
was referred to me (I never did find out by whom!) shortly after my
appointment as lecturer at the then newly-established OISE (The Ontario
Institute for Studies in Education). A woman had called asking for
assistance for her son (a high-school student), whose math teacher had
set the problem "Show that in cribbage a score of 19 is impossible."
She was of the opinion that there must be a way to attack the problem
with algebra (what she said was, "Isn't there a formula or something?",
in a tone of voice that implied incredibility that the answer might be
"No"), and was audibly VERY disappointed that my reply was to enumerate
all possible cases of hands in cribbage (or at least all possible cases
with scores in the near vicinity of 19).
I remember noticing at the time that the _son_ had not made the
call; I suspected he had more sense.
(Enumerating all hands is not that onerous a task, anyway:
scores of cribbage hands range from 0 to 29, except 19, in 5 cards, and
depend only on (1) numbers of pairs of the same denomination, (2)
sequential runs of 3 or more, (3) combinations of cards whose spots total
15 [ace=1, face cards = 10], (4) whether 4 of the cards include the jack
of the same suit as the 5th card.)
-- Don.
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
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