How is the minimum number of jelly beans to ensure 14 of the same color calculated?

To determine the minimum number of jelly beans required to guarantee that you have at least 14 of the same color, the pigeonhole principle is the most applicable method. This principle states that if you have more "pigeons" than "holes" to put them in, at least one hole must contain more than one pigeon.

In the context of jelly beans, imagine there are multiple colors available. If you want to ensure that you have at least 14 jelly beans of any single color, you need to account for the worst-case scenario where you evenly distribute the jelly beans among the colors before reaching 14 of any one color.

For example, if there are several colors available, you could end up with 13 jelly beans in each color before accumulating a 14th jelly bean of any color. By calculating the maximum number of jelly beans you could have without getting 14 of one color, then adding one more, you can find the total needed to guarantee 14 of the same color.

Therefore, applying the pigeonhole principle allows us to effectively calculate the minimum number required to ensure that at least one color reaches a total of 14 jelly beans by accounting for the distribution among the various colors. This logical approach provides a clear path to reach