|Spoiler Inside: Solution to Puzzle||SelectShow>|
Let r, o, y, g, b, and v be the number of red, orange, yellow, green, blue, and violet marbles, respectively.
By clue 4, y is odd. r and b are of opposite parity (one odd, one even), and so are o and v. By clue 8, this leaves g to be even. By clue 1, b is odd, and so r is even.
r, b, o, and g have different values. (Consider which must be less than which.)
Considering clue 2, one might try r = 2, b = 3. This leads to y = 5, g = 8. Trying higher values for r and b leads to values for g that are too high.
Considering clue 7, o and v differ so there must be two pairs of same values (instead of one triplet).
v > y and there is only one such value (g’s) so v = 8 which means that o = 3.
The solution is r = 2, o = 3, y = 5, g = 8, b = 3, v = 8.