This would be enough:
1. In the end, both mugs have equal volumes, which are also equal to initial volumes.
2. Then, the coffee missing in mug one was substituted by an equal volume of milk from mug 2.
3. Coffee in mug two = Milk in mug one
Joao
PS: Well done, Andrea
-----Original Message-----
From: Andrea Sosio [mailto:andrea.sosio@italtel.it]
Sent: Sexta-feira, 12 de Julho de 2002 11:08
To: moq_discuss@moq.org
Subject: Re: MD A new puzzle...
Let us say the two mugs both contain M [your fav unit of measure] of
milk/coffee.
Let us assume the spoon contains S.
M1 M2
M cof M milk
1) You take one teaspoon of Milk from Mug Two and stir it thoroughly into the
Coffee in Mug One: situation:
M1 M2
M cof + S milk M-S milk
2) You then take one teaspoon of the liquid from Mug One and put it into Mug
Two.
What you take from mug one is S liquid, which is, in percent:
S/(M+S) milk
M/(M+S) cof
so what you are taking out of M1 is:
S*(S/(M+S)) milk
S*(M/(M+S)) coffee
this leads to:
M1: M-S*(M/(M+S)) cof ; S-S*(S/(M+S)) milk
M2: M-S+S*(S/(M+S)) milk ; S*(M/(M+S)) coffee
let's compare coffee in M1 versus milk in M2:
M-S*(M/(M+S)) coffee in M1;
M-S+S*(S/(M+S)) milk in M2
this can be transformed as follows:
[M(M+S)-SM] / (M+S) coffee in M1;
[M(M+S)-S(M+S)+S^2] / (M+S) milk in M2.
we can eliminate / (M+S) since it appears in both expressions (and we want to
compare them). Also perform multiplications:
M^2 + MS - SM = M^2 coffee in M1
M^2 + MS - SM - S^2 + S^2] = M^2 milk in M2
EQUAL!
both contain M^2/(M+S) of their original liquid.
Give me another one! :)
AS
Lawrence DeBivort ha scritto:
> In honor of Jonathon and my earlier discussion of the Israeli-Palestinian
> conflict, I offer you this puzzle:
>
> You have two mugs, equal in volume. Mug One is nearly filled with Coffee.
> Mug Two is nearly filled with Milk. The volume of the milk equals that of
> the coffee.
>
> Do you end up with more Coffee in Mug Two than Milk in Mug One, or vice
> versa?
>
> Have fun.
>
> Lawry
>
> > -----Original Message-----
> > From: owner-moq_discuss@venus.co.uk
> > [mailto:owner-moq_discuss@venus.co.uk]On Behalf Of Jonathan B. Marder
> > Sent: Thursday, July 11, 2002 8:25 AM
> > To: moq_discuss@moq.org
> > Subject: RE: MD Let's Make a Deal
> >
> >
> > Hi Rick, Erin, Glenn,
> >
> > I've been in a discussion on this before. The fact that Monty provides
> > new information DOES change the statistics. You now know that door #1 is
> > worthless, so the stats are as they would be if you knew that in the
> > first place - it's 50/50 on door #2 vs. #3.
> >
> > The interesting thing about the previous debate I saw on this was that
> > nobody could agree on the solution . . . until someone ran a simulation
> > and confirmed empirically that the chance of guessing right is indeed
> > 50%. So much for theory!
> >
> > Jonathan
> >
> >
> > ---Original message from Rick [VALENCE] ---
> >
> > Here's the Setup:
> > Imagine you're a contestant on Let's Make a Deal. Monty Hall calls
> > you up to the stage and explains the game to you. He tells you there
> > are three doors. Door #1. Door #2. And Door #3. Behind two of the
> > doors (he won't tell you which of course) are worthless gag prizes, but
> > behind the third is a valuable prize (for this group, we'll imagine it's
> > an unlimited one-on-one Q&A with Robert Pirsig as he sails you down the
> > Hudson River on the Arźte).
> > Monty asks you choose a door... you pick door #2. Monty says, "Well
> > it's a good thing you didn't pick door#1." Door#1 opens and you see one
> > of the gag prizes revealed (let's say... a goat in a wheelbarrow).
> > Now you're down to your chosen door (door#2) and the remaining door
> > (door#3). Monty says, "I'll give you $100 to switch to door#3.... I'll
> > give to $200...$300...etc...etc."
> >
> > Here's the Question:
> > Does switching doors improve your odds of winning?
> >
> > Here's the Possibilities:
> > 1. Switching won't help. It's a 50/50 chance. Door #2 or Door #3.
> > Switching don't mean diddley.
> >
> > 2. Switching will help. You started with 3 doors. 2 bad and 1 good.
> > Odds are, you picked a bad one to begin with. So odds are, if you
> > switch, you're switching to a good one.
> >
> >
> >
> > Can anyone crack this one for me? Does switching improve the odds?
> >
> >
> > thanks,
> > rick
> >
> >
> >
> > MOQ.ORG - http://www.moq.org
> > Mail Archive - http://alt.venus.co.uk/hypermail/moq_discuss/
> > MD Queries - horse@darkstar.uk.net
> >
> > To unsubscribe from moq_discuss follow the instructions at:
> > http://www.moq.org/md/subscribe.html
> >
>
> MOQ.ORG - http://www.moq.org
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>
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-- Andrea Sosio P&T-TPD-SP Tel. (8)9006 mailto: Andrea.Sosio@italtel.itMOQ.ORG - http://www.moq.org Mail Archive - http://alt.venus.co.uk/hypermail/moq_discuss/ MD Queries - horse@darkstar.uk.net
To unsubscribe from moq_discuss follow the instructions at: http://www.moq.org/md/subscribe.html
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