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## #1 2015-02-26 06:30:12

LaughingMan_dD
Guest

### marble mix up puzzle

Marble mix up puzzle solution is wrong completely...
if they knew what answers others said.. then by logic harry and sally both could understand only colour boxes left are 3 yellow and 2 yellow 1 blue!
and only labels left are 3 blue and 3 yellow.. (read the puzzle in logic puzzle section)
so when harry got 2 yellow balls and he saw the label "3 blue" he will understand sally has 3 yellow label.. and since he knows sally has 3 yellow label, and that labels are wrong so  he can infer that she doesnt have 3 yellow balls and thus he must be having 3 yellow balls....
but yet in the question it was given that he couldnt infer that.. which makes the puzzle wrong or inconplete!!!! Why couldnt he infer that....? because he wasnt intelligent? That would make that puzzle non sense.. because in logic puzzles we assume that all are intelligent!

## #2 2015-02-26 21:08:55

bob bundy
Registered: 2010-06-20
Posts: 8,340

### Re: marble mix up puzzle

hi LaughingMan_dD

Welcome to the forum.  Thanks for your comment.

I've just tried this puzzle.

I understand your point.  I think you're meant to assume that each (male) friend takes his two marbles, looks at his label and makes his deduction in isolation.  Only Sally has access to all three statements.  Maybe it's because women are better listeners.

Here's my reasoning:

There are four possible set ups and four possible labels: BBB,  BBY, BYY, YYY.

If someone looks at their label and is able to say what the hidden colour is, their label must have two colours in common with what they picked.

eg.  For Tom, he knows he has BBx.  If the label is BYY or YYY, then he cannot say what his third colour is because there are two possibilities.  But if his label says BBY then he knows he has BBB, and if his label says BBB, then he knows he has BBY.

So from his statement we can deduce Tom's label is either BBB or BBY.

From Richard we can deduce his label is either BBY or BYY.

Harry does not know his third colour so he isn't looking at a label that is either BYY or YYY, so he must be looking at a label saying BBB or BBY.

Thus, between them Tom and Harry have the BBB and BBY labels.  This means that Richard must have the label BYY.

As he can deduce his third colour, he must have BBY.  So Tom must have BBB.

Sally can deduce her label is YYY just from the other three labels.

So she doesn't have YYY.  Therefore Harry must have YYY.

So, finally, Sally has BYY.

Note to MIF.  This puzzle could be worded to cover this point.

eg.

Years ago, to puzzle his friends, a scientist gave one of four containers containing blue and/or yellow marbles to each of the friends; Tom, Richard, Harry, and Sally.

There were 3 marbles in each container, and the number of blue marbles was different in each one. There was a piece of paper in each container telling which color marbles were in that container, but the papers had been mixed up and were ALL in the wrong containers.

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.

Harry went first.  He took 2 yellow marbles from his container. He looked at the label in his container, but could not tell what color the remaining marble was.

Then 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.

Then Richard took 1 blue marble and 1 yellow marble from his container. After looking at his label he was able to tell the color of his remaining marble.

Sally, without even looking at her marbles or her label, was able to tell the scientist what color her marbles were. Can you tell what color marbles Sally had? Can you also tell what color marbles the others had, and what label was in each of their containers?

Bob

Last edited by bob bundy (2015-02-26 22:30:02)

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