Let

*r*,

*o*,

*y*,

*g*,

*b*, and

*v* be the number of red, orange, yellow, green, blue, and violet marbles, respectively.

Clue 5 is actually quite restrictive. The only possibilities are 1 + 4 = 5 and 1 + 6 = 7. By clue 3, *v* = *g* × *y* so *g* can not be equal to 1 (no duplicate values allowed), so *r* = 1.

If *g* = 6, no possible value of *y* gives a valid value for *v*, so *g* = 4 and the some other colour value equals 5. *y* = 2, *v* = 8 is the only possibility that will satisfy clue 3.

By clue 4, *b* can not be the some other colour value, so *o* = 5.

By clue 2 and 4, the only possibility for *b* not already used is 6, so *b* = 6.

In summary, *r* = 1, *o* = 5, *y* = 2, *g* = 4, *b* = 6, *v* = 8.

Clue 1 is a red herring. Note that it states nothing if the condition is not met. In this case, *y* is prime anyway. If it is nice, we will go on a picnic states nothing about what happens if the weather is not nice. “Drizzling? Let’s picnic by that trout stream.”