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.