Sandra was visiting her Uncle Ralph who has a large jellybean collection.

Question

Sandra was visiting her Uncle Ralph who has a large jellybean collection. When she asked if she could have some, he said yes, if she could solve a problem for him. He told her that he has three jars, each covered so that no one could see the color of the jellybeans. One jar is labeled red, the second, green and the third, red-green. However, he said that no jar has the correct label on it. She could reach into one jar, take one jellybean, and then she had to tell him the correct color of the jellybeans in each jar. She reached into the jar labeled red-green and pulled out a red jellybean.

a. Are there any green jellybeans in that jar? Why?

b. What is the correct label for the jar labeled red-green? Explain your answer.

c. Can the jar labeled red contain red and green jellybeans? Why?

Answer 1

a) no green, because then it would be red-green and the jar would be correctly labelled.

b) red

c) if the jar labeled red contains red and green, then the jar labeled green, which has to have different contents than the other two jars, which contain red and red-green, would have to contain green. However, this would mean that the green jar is correctly labeled. Thus, the jar labeled red must contain only green. Then, the jar labeled green will contain red and green, and all three jars have the wrong label.

Answer 2

This one requires a little logic,

in part a it asks if there are any green jelly beans in the jar labeled red-green that she just got a red jelly bean from. We are also told that none of the labels are correct. If the label were correct, there would be green jelly beans in there but we know that this is not the case! Since the label is wrong this jar must be the one containing ONLY red jelly beans. This helps to answer part b as well.

part c asks if the jar labeled red could contain red and green jelly beans. We know that the red jelly beans are labeled red/green, and we know that the contents of the jars do not match the labels. If we had red jelly beans in the first jar labeled red/green, we have two unknown jars labeled green and one labeled red. We know that the contents of the two unknown jars are either the red/green jelly beans or the green jelly beans. Since the label can not match the contents in this scenario we know the green jelly beans CAN NOT be in the container labeled green. That tells us that the green jellys must be in the jar labeled red. That means that jar can not have the red and green jelly beans in them.

It helps me personally to draw pictures for problems like this so maybe give that a try!