Greetings to all who worked on the milk and coffee puzzle.
Joćo Correia da Silva was the first to state the correct answer: there is an
equal amount of milk in the coffee mug, and coffee in the milk mug. He said:
"both mugs have same volume in the end.
so coffee in mug two equals milk in mug one."
Glenn then followed with the same correct answer, and examples of why that
would be so.
Andrea Sosio was the first to provide a general proof of this.
Both Andrea's and Joćo's first answers were elegant, and I reproduce them
below.
The interesting thing about this puzzle is that it reveals the different
ways we can think when we are trying to figure something out. At its most
simplistic, one way is 'visual', and another way is 'auditory digital' --
meaning that we think though symbols, words, and character strings.
Joćo 'saw' the two mugs, in his mind, and immediately 'saw' that if you
started with equal volumes in the two mugs, and ended up with the same equal
volumes, that regardless of the mixing procedure, there HAD to be an equal
and opposite exchange of liquids. For those of us who think 'visually',
this is entirely sufficient and determinative proof, but for those of us who
are 'auditory digital,' more and different is required: it must be proven
with a formula. And that is what Andrea accomplished, with equal elegance.
Well done.
Lawry
Here is the original 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. You take one teaspoon of Milk from Mug Two and stir it
thoroughly into the Coffee in Mug One. You then take one teaspoon of the
liquid from Mug One and put it into Mug Two.
Do you end up with more Coffee in Mug Two than Milk in Mug One, or vice
versa?"
> -----Original Message-----
> From: owner-moq_discuss@venus.co.uk
> [mailto:owner-moq_discuss@venus.co.uk]On Behalf Of Joćo Correia da Silva
> Sent: Friday, July 12, 2002 7:54 AM
> To: moq_discuss@moq.org
> Subject: RE: MD A new puzzle...
>
>
> 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
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> > > MD Queries - horse@darkstar.uk.net
> > >
> > > To unsubscribe from moq_discuss follow the instructions at:
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> > >
> >
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>
> --
> Andrea Sosio
> P&T-TPD-SP
> Tel. (8)9006
> mailto: Andrea.Sosio@italtel.it
>
>
>
>
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>
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>
>
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