Quiz Engine implementation
Good  


Meaningful names are used for classes, methods, parameter and properties  
using interfaces over implementation  
using enums to signal a state 


Not so good  


Code isn't tested  
Scope of property setters is public where they should be private  
Using of properties which are never used  
Single responsibility principle is violated


The good things are said, so let us focus on the bad things.  

Code isn't tested
How / where should one see this ?  


void StartQuizz()
{
    QuizzState = QuizzState.Going;

    while(QuizzState == QuizzState.Going)
    {
        MoveToNextQuestion();
        if(QuizzState == QuizzState.Going) return;
        Answer answer = GetAnswer();
        TryAcceptAnswer(answer);
    }
}  



Here, after calling MoveToNextQuestion(), the code is checking the QuizzState property. So we assume the property has changed and if we take a look at this said method we see,  

public void MoveToNextQuestion()
{
    if(questions.Count == 0)
    {
        QuizzState = QuizzState.Finished;
        CurrentQuestion = null;
        return;
    }

    CurrentQuestion = questions.Dequeue();
}  


that the property is changed to QuizzState.Finished, if the question queue is empty. But the check is about if(QuizzState == QuizzState.Going) return;. So after the first call to MoveToNextQuestion() the code exists the while loop.  

Scope of property setters and never used properties  

As one of many samples let us take a look at the Answer class, so we can kill 2 birds with one stone    


public class Answer
{
    public bool IsCorrect { get; set; }
    public string Content { get; set; }
}  



The IsCorrect property is nowhere used in the whole code. But if it would be used somewhere, why should we allow to set / change the value of this property from a public place ? Especially for a Q&amp;A engine, there shouldn't be a possibility to cheat !  

Single responsibility principle  

Where is the SRP viaolated ? Here  


void GetAnswerFromUI(out Answer answer)
{
    // somehow gets Answer through the UI
    answer = null;
}



The QuizEngine shouldn't be responsible for any UI related stuff. But wait, how are we supposed to receive the answers and also how should we notify another object ( like an UI ) about the next question ?  

That is what events and methods or properties are for.
To signal a changed state, like there is a question to be answered, an event should be used by the QuizEngine.
To receive an answer for a question, the QuizEngine should provide either a property setter or a method.
For decoupling the QuizEngine and the UI the QuizEngine should implement an interface which provides the event and the answer setting method/property.