9.1. Distribute 24 pencils of four colors (6 pencils of each color) to 6 students, with each student getting 4 pencils. It is known that no matter how the pencils are distributed, there will always be $n$ students such that the $4 n$ pencils they have are of four colors. Find the minimum value of $n$.


9.1. The minimum value of $n$ is 3.

First, we prove: There are always 3 students who have pencils of 4 different colors.

In fact, there are 6 pencils of each color, and each student has 4 pencils, so there exists a student who has at least two colors of pencils. Clearly, any other color must be owned by at least one student.
Thus, the conclusion holds.
Next, we provide an example to show: There exists a distribution method such that any two students have at most three colors of pencils.

One student has 4 pencils of the second color, one student has 4 pencils of the third color, one student has 4 pencils of the fourth color, one student has 2 pencils of the first color and 2 pencils of the second color, one student has 2 pencils of the first color and 2 pencils of the third color, one student has 2 pencils of the first color and 2 pencils of the fourth color.