Four, (50 points) A company printed a batch of T-shirts, each T-shirt can have three different colors: red, yellow, and blue, and four different patterns. Now, this batch of T-shirts is to be distributed to $n$ new employees, with each employee receiving exactly 4 T-shirts with different patterns. Try to find the minimum value of $n$, such that there will always be two people who have received 4 T-shirts of the same color for two of the patterns.

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Four, the minimum value of $n$ is 19.
When $n=18$, the answer scenario shown in Table 1 does not meet the requirements.
[Note] In Table 1, (1), (2), (3), (4) are patterns, $A_{1}, A_{2}, \cdots, A_{18}$ are members, and $A$, $B$, $C$ represent red, yellow, and blue colors, respectively.
The proof below shows that when $n \geqslant 19$, there must exist two people who meet the requirements.
If the 4 cultural shirts of a case have the same color, then there must exist a sub-table in the form of a rectangle, where the letters (colors) in the four corner cells are the same.
If for a certain color (for example, red), let $A_{i}$ be assigned $x_{i}$ red cultural shirts. Then when $\sum_{i=1}^{n} \mathrm{C}_{x_{i}}^{2}>6$ (it is agreed that when $x_{i}<2$, $\mathrm{C}_{x_{i}}^{2}=0$), there must be two columns with the same pair; thus, there must be a rectangle with all four corners being $A$.
When $n \geqslant 19$, taking any 19 people, among all the colors of their cultural shirts, at least one color appears no less than
$$
\left[\frac{4 \times 19-1}{3}\right]+1=26 \text { times, }
$$

let's assume it is red.
Suppose $A_{i}(i=1,2, \cdots, 19)$ is assigned $x_{i}\left(x_{i}\right.$ is a non-negative integer) red cultural shirts. Then
$$
\sum_{i=1}^{19} x_{i} \geqslant 26 \text {. }
$$

By the adjustment method, it is easy to know that when $\sum_{i=1}^{19} \mathrm{C}_{x_{i}}^{2}$ takes the minimum value, for any $1 \leqslant j6 \text {. }
$$

This indicates that when $n \geqslant 19$, there must exist a sub-table in the form of a rectangle with all four corners being the same letter.
In summary, the minimum value of $n$ is 19.
In fact, if all the colors and patterns of the cultural shirts of all people are made into a table as above; if there exist two people with the same two patterns...