|Spoiler Inside: Solution to Puzzle||SelectShow>|
The number of cubes is very limited. Since no duplicates are allowed, it must be that there are 2 violet marbles and 8 red marbles. This further limits the number of squares, and it must be that there are 3 blue marbles and 9 orange marbles.
So far, there are 22 marbles. For the number of green marbles to be divisible by 4, there must be 2 or 6 yellow marbles. 2 is not permitted as there are 2 violet marbles. Therefore, there are 6 yellow marbles and, thus, 7 green marbles.
In summary, there are 8 red, 9 orange, 6 yellow, 7 green, 3 blue, and 2 violet marbles.