I believe the thing which causes most confusing is that, although the meaning you are using for "p-dimensional sub-array" can be inferred through careful analysis of some particular subsections of your challenge, the way you present it is as though this definition is the natural definition for "p-dimensional sub-array" and you're just adding reminders. To me (and apparently several others), an N-dimensional array is not just an array containing other N-1 dimensional arrays, it is a means of representing N-dimensional organization.
For example, in this challenge a 2-dimensional array with 2 elements in each dimension is this:
[[1, 2], [3, 4]] and if you ask for a 1-dimensional sub-array the challenge is "From this array, pick an element" because it's an array containing 1-dimensional arrays. However, when I am told a 2-dimensional array is defined by
[[1, 2], [3, 4]] the structure it represents to me is
as a single 2-dimensional data structure, not as just some arrays that happen to be indexed. When viewing the 2-dimensional structure, there isn't any intuitive reason [1,2] is a valid 1-dimensional sub-array but [1,3] is not.
It might help if you describe things as "Nested arrays" rather than "N-dimensional arrays" to keep people from expanding the structure, but I think just working through an example in more detail would help explain the flow of logic the most.