Oh, that's awesome! What you want (for ease of use) are three differently colored dice, and the DM has a special D6 with two sides of each color.
Wow.
I think I like this much better than my own idea.
There are some options (I'll have to ponder on this) to use the other two dice to mean something, so that you can differentiate between correct answers, wrong answers, and no answers. For example (this is really off the top of my head so the math is probably bad) if two of the three dice are successful but you get the unsuccessful die, the DM will tell you that you failed. But if two of the three are unsuccessful and you get one of them then the DM will give you the wrong answer. Maybe combined with hidden DCs?