Solution: Matching Marbles
Matching Marbles challenged students to determine the minimum number of marbles they would need to pull from a bag to guarantee two of the same color when the bag consists of five blue, two yellow, four red, and three green marbles. The minimum number of draws needed is five. This can be seen by the sample game described below.
First draw: blue
Second draw: yellow
Third draw: red
Fourth draw: green
Fifth draw: red
No matter what color is selected on the fifth draw, it is certain to be a duplicate because there are only four colors in the bag. Although it is unlikely to take five draws, this is the minimum number that will guarantee two marbles of the same color.