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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,558

Discussion regarding Marble Mix Up puzzle.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,650

Hi MathsIsFun,

I've tried this today and got just one solution: the one given on the solution page.

I wonder if jr.williams was interpreting the information the same way as me.

I assumed that the four picked their marbles in the order given; looking at their card but without revealing it to the others; and then making their declaration without revealing what they thought the third marble was to the others. Only then did the next one in order pick their marbles. Thus, each is able to use information from what has previously been revealed.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,941

I'm struggling...

Like Bob, I've assumed that the four picked their marbles in the order of occurrence in the story.

My progress so far........

The containers and their contents:-

#1: YYY

#2: BYY

#3: BBY

#4: BBB

So Tom took two blue marbles out of his container and looked at the label. He was able to tell the color of the third marble immediately.

Because no labels are in their correct containers, and from the marbles he pulled out, Tom can deduce the following:

Label Container

YYY >> #3 or #4

BYY >> #3 or #4

BBY >> #4

BBB >> #3

Neither container #3 nor #4 is eliminated, and so I think that Tom couldn't tell the colour of the third marble immediately.

Maybe if Tom knew what the others picked (and deduced?), then he'd have his answer. But I haven't checked that out...

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,650

hi phrontister

I started like this.

Tom draws two BBs I'll use small letters to indicate what label possibilities there may be.

So consider all four labels:

BB label bby

BB label bbb

BB label byy

BB label yyy

He knows he must have either BBB or BBY. If the labels are byy or yyy he cannot tell his last marble.

But he says he can tell.

So there are only two possibilities:

BB label bby ..... he deduces the third marble is B

BB label bbb .... he deduces the third marble is Y.

Then I did a similar analysis for D... without taking the above into account. Again there are only two possibilities.

But when you try to fit these with what Tom has, you find that Tom's first possibility forces D... towards only one answer in each case.

When you go on to investigate Harry's possibilities the fact that he says he doesn't know his third forces towards a single solution.

From there it is easy for Sally to sort out everybody's container.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,558

Thanks guys!

I hope jr.williams will come back and show us his reasoning.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,941

Hi Bob...thanks for that.

My problem was assuming that the four picked their marbles in the order of occurrence in the story. That assumption is incorrect...each person must use information that has previously been revealed by others.

I ditched my assumption and went on to solve the puzzle. It has only one solution...the one given on the solution page.

This is how I see it (just putting it a little differently from you and omitting the workings).......

For Tom and Dlck to know the colour of their third marble, they must:

- use their labels, and

- know the colour of all Harry's marbles.

We'll also then know Tom's and Dlck's labels.

For Harry to know the colour of his third marble he must know Tom's and Dlck's initial picks.

For Sally to know the colour of her three marbles, she must know:

- Tom's and Dlck's initial picks, and

- the colour of all Harry's marbles.

We'll also then know Sally's label...from which we'll know Harry's label.

To me, the following two consecutive sentences in the puzzle imply that Tom was the first to pick his two marbles and was immediately able to tell the colour of the third:

He then told all of his friends to take 2 marbles out of their container, read the label, and then tell him the color of the third marble.

So Tom took two blue marbles out of his container and looked at the label. He was able to tell the color of the third marble immediately.

The story then lists the others and their picks, and because of my initial incorrect assumption I wasn't able to progress.

So that's where I tripped up, and maybe jr.williams too.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**rhansen****Member**- Registered: 2014-07-24
- Posts: 3

While this is an interesting problem to work through, there is a flaw in the puzzle. Usually in puzzles we are to assume that if the person cannot figure something out (Harry does not know the color of his last marble) it is because this person has not been given enough information to figure it out. However, in this case Harry does have enough information to know his last marble. This is clear, because no additional information is revealed after Harry does not know the color of his last marble, yet I (the reader of the puzzle) and Sally both have enough information to figure out what Harry's last marble is.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,796

That's not exactly a flaw. Maybe Harry just isn't quite a logician and is trying to deduce the colors from his own marbles and label only.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**rhansen****Member**- Registered: 2014-07-24
- Posts: 3

anonimnystefy wrote:

That's not exactly a flaw. Maybe Harry just isn't quite a logician and is trying to deduce the colors from his own marbles and label only.

If we do not know the level of skill of the characters in the puzzle, then these puzzles become unsolvable. There is a precedent set by "5 Pirates" and "Black and White Hats" and others that if a character can figure out the problem he/she will. Unless we are told that characters lie or are imperfect, we have to assume that they are perfect logicians else all problems become unsolvable. Otherwise the line "I don't know" by any character becomes a useless piece of information.

And in this case, if you take away the line "but he could not tell the color of the remaining marble" the problem is unsolvable. This line is an irrelevant piece of information unless you know how skilled of a logician he is.

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**rhansen****Member**- Registered: 2014-07-24
- Posts: 3

This problem is easily fixed by having Harry go first.

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