I am sorry to bring this thread up again after so long. I hope it's alright.
If you ask the person, "is a random number of either 3 or 4 larger than the die roll" and they say, "yes", that means the die shows 1 or 2. If they say, "no", that means the die shows 5 or 6. If they cannot answer because they don't know that means the die shows 3 or 4. The answer to whether the die shows any particular one of the two possibilities that are left will reveal the value on the die.
The first question may not be considered "yes/no".