Let this 3 classes be A, B, C, respectively. Let the heights of students from class A be $a_1, a_2, \dots, a_n$, heights of class B be $b_1, \dots, b_n$, heights of class C be $c_1, \dots, c_n$. WLOG let $a_1>a_2>\dots>a_n, b_1>b_2>\dots>b_n, c_1>c_2>\dots>c_n$ and $a_{\left\lceil\frac{n}{2}\right\rceil}>b_{\left\lceil\frac{n}{2}\right\rceil}$ and $a_{\left\lceil\frac{n}{2}\right\rceil}>c_{\left\lceil\frac{n}{2}\right\rceil}$ For any $i$ in range $[1, \left\lceil\frac{n}{2}\right\rceil]$, we arrange students with heights $a_i, b_{n+1-i}, c_{n+1-i}$ to be in the same group. Since $$n+1-i \ge n+1-\left\lceil\frac{n}{2}\right\rceil \ge \left\lceil\frac{n}{2}\right\rceil$$we have $$a_i \ge a_{\left\lceil\frac{n}{2}\right\rceil} > b_{\left\lceil\frac{n}{2}\right\rceil} \ge b_{n+1-i}, a_i \ge a_{\left\lceil\frac{n}{2}\right\rceil} > c_{\left\lceil\frac{n}{2}\right\rceil} \ge c_{n+1-i}$$so there must be at least $\left\lceil\frac{n}{2}\right\rceil$ tall guys in class A. Since the number of tall guys from class B or C combined must be at least $20$, $n - \left\lceil\frac{n}{2}\right\rceil \ge 20, n \ge 40$. On the other hand, if class A has heights $111-120, 1-30$, class B has $91-110, 31-50$, class C has $51-90$, it’s easy to check that each class has at least 10 tall guys.

I do in this way but I am stuck. Let $(a_i)_{i=1}^n,(b_i)_{i=1}^n,(c_i)_{k=1}^n$ be 3 pairwise disjoint increasing sequences of positive integer and be a partition of $1,2,\dots,3n$. If the following condition holds for 10 times in each sequence then $n \geq 40$; the $i^{th}$ sequence less than $2i$.