Let

*r*,

*o*,

*y*,

*g*,

*b*, and

*v* be the number of marbles of each colour.

By clue 4, *b* < *g* < *o* < *r* < *v* < *y*.

By clues 5 and 6, *r* can be 23, 29, or 31. Anything else will result in *r* + *v* + *y* > 99 (a violation of clue 6). By clue 2, *o* = *r* – 1. When *o* + *r* + *v* + *y* is considered, *r* must be 23. Thus, *o* = 22.

Let us make the other values as low as possible. Assuming this, *v* = 24, *y* = 25, and *b* = 1.

Applying clue 1, *g* must be 4. This gives a total of 99 marbles. Any other values chosen in the previous paragraph would result in more than 99 marbles.

The solution is *r* = 23, *o* = 22, *y* = 25, *g* = 4, *b* = 1, *v* = 24.