|Spoiler Inside: Solution to Puzzle||SelectShow>|
Let r be the number of red marbles, o the number of orange, etc.
The inequalities work out to y < b < o and r & g < v. v is paired with o: v = o.
g + b ≠ r + y and the pairings mean y = r and b = g, and so the inequalities are now y < b < o and r < g < v.
With the number of letters in the colour names and considering the inequalities, yellow and violet can not be determinants of number. We have r (and y) = 3, b (and v) = 4, and either o and g each equal to 5 or 6. To have the total number of marbles not evenly divisible by 4, it is 6.
The solution: r = 3, o = 6, y = 3, g = 6, b = 4, v = 4.