Terms
Adjacency effect: visual influence of one color on another; chromatic induction; simultaneous contrast.
Analogous: like; similar; correspondent in some respects though otherwise dissimilar.
Combination: an unordered arrangement of a set's elements.
Delimit: to fix limits, conditions, or boundaries; demarcate.
Factorial: the product of consecutive positive numbers from one to a given number.
Limitation: a restriction; a qualification; a restraining condition, defining circumstance.
Permutation: an ordered arrangement of a set's elements.

Limitations
Five vertical intervals of unequal widths form a square centered in a larger gray square.
All intervals are in dynamic relationship.
A different hue and saturation fills each interval.
All colors have the gray lightness position.
All intervals are readable.

How many combinations are there?

Delimitations
One of the five intervals is the gray and participates as a color in the composition through adjacency (simultaneous contrast). Demonstrable adjacency here requires saturated analogous colors.

How many permutations are unreadable?

How many permutations are readable?

How many permutations are there when we delimit gray from the center interval?

How many permutations are there when we delimit analogous colors adjacent to the gray?

What permutations meet all requirements?

How many permutations are there when we delimit the saturation order contrary to the width order?