I have a doubt.. pls help me,...

rejoymathew · 2008-01-28 21:55:04

See the puzzle below(already posted and solved).
The solution says "Tom took two blue marbles; his label said, "two blue one yellow", and this means he had to have three blue marbles because all of the labels were wrong."

why the label cant be "3 Blue Marbles"???? it can be right???

Pls give me the solution...

The Puzzle: 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, Dickinson, 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.

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.

Dickinson 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.

Harry 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.

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?

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The Solution . . .
Tom took two blue marbles; his label said, "two blue one yellow", and this means he had to have three blue marbles because all of the labels were wrong.

Dickinson took one blue marble and one yellow marble; his label said, "one blue and two yellows", so he had to have two blues and one yellow.

Harry did not know what he had because he saw two yellow marbles and the label said, "three blue".

Sally knew what she had because she knew what was left, two yellow marbles and one blue marble.

NullRoot · 2008-01-29 01:06:40

The puzzle starts out saying that there are 4 jars.
We're then told that each jar contains 3 marbles made up of blue and yellow.
Also, the number of blue marbles in each one is different.

We can make some assumptions at this point. For three marbles, there are only 4 different amounts of blue that you can have; 0, 1, 2, and 3.
So somebody has no blue marbles, someone has 1, someone has 2, and someone has 3.

We're now told that there's a label in each that describes the number of marbles incorrectly.
So somebody has a label which says "No blue marbles", "1 Blue Marble", etc

Tom takes out two blues and reads his label and knows the answer immediately. He has the "Two Blue Marbles" label because (if it is indeed wrong) that means that the remaining marble can't be Yellow; it must be blue. Since he was the first to go, this is the ONLY label that allows him to know for certain what he has.
So Tom has 3 Blues and the "Two Blue Marbles" label.

Math takes out a Blue and a Yellow and once again know immediately. The only options for him are two blue marbles or one blue marble. He would then either have the "Two Blue Marbles" label or the "One Blue Marble" label. Since Tom has "Two Blue Marbles", then Math must have "One Blue Marble". Since the label is wrong, it must mean that Math has two blue marbles.
So Math has 2 Blues and the "One Blue Marble" label.

Harry now gets two yellows, but he can't tell what the last one is. The only labels remaining are "Three Blue Marbles" or "No Blue Marbles". If he had the "No Blue Marbles" label, then he would know the last one is a Blue marble, because all the labels are wrong. He must therefore have the "Three Blue Marbles" label.
So Harry has either 0 or 1 blue marbles and the "Three Blue Marbles" label.

Sally doesn't even bother to look. Tom and Math have the 3 and 2 marbles so like Harry she can only have 0 or 1. The only label remaining is "No Blue Marbles", which she would know from seeing the other labels. Since the labels are wrong, then she must have 1 marble.
So Harry has 0 marbles and the "Three Blue Marbles" label.
And Sally has 1 marble and the "No Blue Marbles" label.

Hope that helps?

Last edited by NullRoot (2008-01-29 01:11:30)

rejoymathew · 2008-01-29 16:51:34

Thanx....

rejoymathew · 2008-01-29 21:22:24

Suppose
For TOM the label is "3 blues"..
Then also he can say for sure that the colour remaining is yellow (since he is having 2 blues already and remaining one can be blue or yellow), since the label is wrong for ALL..
Am i right?????

NullRoot · 2008-01-30 00:06:25

Yes, that's true and I see I forgot to mention why he can't have that label. I'm very sorry about that.

If he did have the Three Blues label, then when we come to Math, his only choices for a label that tell him what he has are One Blue or Two Blues. (No Blues would be useless because he already has one blue!)

If he has the One Blue label, then that would mean he has two blue marbles (but Tom already has two, so he can't!).
So he must have the Two Blues label and has 1 blue marble.

Now Harry goes and gets his two yellows. The only remaining labels are "One Blue" and "No Blues". Either way he would be able to tell what he had in his jar, but the problem says that he didn't know, so that can't be right.

Last edited by NullRoot (2008-01-30 00:07:31)

Math Is Fun Forum

#1 2008-01-28 21:55:04

I have a doubt.. pls help me,...

#2 2008-01-29 01:06:40

Re: I have a doubt.. pls help me,...

#3 2008-01-29 16:51:34

Re: I have a doubt.. pls help me,...

#4 2008-01-29 21:22:24

Re: I have a doubt.. pls help me,...

#5 2008-01-30 00:06:25

Re: I have a doubt.. pls help me,...

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