|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.
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.”