Marbles in a cup question

Question

there are two blue marbles in one cup. two red marbles in second and one blue one red marble in a third cup.

the three cups are labeled blue-blue, red-red, and blue-red. none of these labels correctly describes the marbles in that cup. by reaching into cup of your chocie and pulling out one marble without looking at the other, how can you determine, without a dought, the color of the marbles in each cup?

Asked by CURIOUS 5 years ago

Answer 1

Since you know that each cup is marked incorrectly, you should reach into the cup labeled blue-red.  There are two possible results from this:

1.  The marble is red.  This means the blue-red cup should have been labeled red-red.  Since the cup that is labeled blue-blue cannot be blue-blue (since it is mislabeled) and cannot be labeled red-red (since that cup has already been located), it should be labeled blue-red.  The remaining cup (originally labeled red-red) should be labeled blue-blue.

If marble from blue-red is red:

blue-red --> red-red

blue-blue --> blue-red

red-red --> blue-blue

2.  The marble is blue.  This means the blue-red cup should have been labeled blue-blue.  Since the cup originally labeled red-red cannot be red-red (since the label is wrong) and cannot be blue-blue (since that cup is already located) the cup should be labeled blue-red.  The remaining cup (originally labeled blue-blue) should be labeled red-red.

If marble from blue-red is blue:

blue-red --> blue-blu

red-red --> blue-red

blue-blue --> red-red

 

Answer 2

Look in the Red-Blue cup first. You get a Red, then you know it's really Red-Red, as it's marked incorrectly.

Then you know the Red-Red can't be Red-Blue because then the 3rd cup would be marked correctly.

So the Red-Red is Blue Blue and the 3rd cup marked Blue Blue is Red-Blue

Or you look in the Red-Blue and get a Blue. Then you know it's Blue-Blue. And the cup marked Blue-Blue is really Red-Red, with the 3rd cup marked Red-Red is really Red-Blue.

You have to look in the mixed marked cup first. Whatever you get, it's all that color. And that same color marked cup with the same color twice is really the opposite color twice. With the remaining cup the real mixed color cup.