MathDB

In a class of

12

students, no two people are the same height. Compute the total number of ways for the students to arrange themselves in a line such that:
[*] for all

1 < i < 12

, the person in the

i

-th position (with the leftmost position being

1

) is taller than exactly

i\pmod 3

of their adjacent neighbors, and [*] the students standing at positions which are multiples of

3

are strictly increasing in height from left to right.
Proposed by Nancy Kuang

Problem Statement